Physical Science Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

The speed at which light travels depends directly on the optical density and refractive index of the medium through which it passes. Arrange the following media in order of the speed of light within them, from slowest to fastest.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

Diamond, Crown glass, Liquid water, Vacuum (from slowest to fastest)

Light travels fastest through empty space (

c \approx 3.00 \times 10^8\text{ m/s}

) where the refractive index is

1.00

. When entering denser transparent media, the wave interacts with the electromagnetic fields of atoms, causing an apparent slowdown proportional to the medium's index of refraction (

v = \frac{c}{n}

). Diamond has the highest index of refraction among the options (

n \approx 2.42

), making it the slowest, followed by crown glass (

n \approx 1.52

), liquid water (

n \approx 1.33

), and vacuum (

n = 1.00

).

Step-by-Step Solution

1

Identify the relationship between the index of refraction and the speed of light.

The speed of light in a medium is inversely proportional to its refractive index, given by

v = \frac{c}{n}

, where

c

is the speed of light in a vacuum and

n

is the refractive index.

Higher refractive indices indicate greater optical density and slower wave propagation speeds.

2

Rank the media by their refractive indices from highest to lowest.

Diamond (

n \approx 2.42

) > Crown glass (

n \approx 1.52

) > Liquid water (

n \approx 1.33

) > Vacuum (

n = 1.00

).

Ranking from highest index to lowest index establishes the reverse order of speed.

3

Invert the refractive index ranking to order the media from slowest speed to fastest speed.

Diamond (slowest,

\approx 1.24 \times 10^8\text{ m/s}

)

\rightarrow

Crown glass (

\approx 1.97 \times 10^8\text{ m/s}

)

\rightarrow

Liquid water (

\approx 2.25 \times 10^8\text{ m/s}

)

\rightarrow

Vacuum (fastest,

\approx 3.00 \times 10^8\text{ m/s}

).

Matches the required sequence criteria from slowest to fastest.

Key Concept

Inverse relationship between index of refraction and wave speed in optical media (

v = \frac{c}{n}

)

Estimated Time:1m 0s

Question 2Question →

A sound wave traveling through air at a constant temperature has a frequency of $250\text{ Hz}$ and a wavelength of $1.36\text{ m}$ . If the frequency of the sound source increases to $500\text{ Hz}$ , what is the new wavelength of the sound wave?

2.72\text{ m}

1.36\text{ m}

0.68\text{ m}

0.34\text{ m}

Show answer & explanation

Answer: $0.68\text{ m}$

Answer

The new wavelength is

0.68\text{ m}

.

Wave speed in a given medium at constant temperature is constant (

v = f\lambda

). The initial speed is

250\text{ Hz} \times 1.36\text{ m} = 340\text{ m/s}

. When the frequency doubles to

500\text{ Hz}

, the wavelength must be halved:

340\text{ m/s} \div 500\text{ Hz} = 0.68\text{ m}

.

Step-by-Step Solution

1

Calculate the constant wave speed in air using the initial conditions

v = f_1 \times \lambda_1 = 250\text{ Hz} \times 1.36\text{ m} = 340\text{ m/s}

The speed of a mechanical wave depends entirely on the medium and remains constant at a fixed temperature.

2

Rearrange the wave equation to solve for the new wavelength

\lambda_2 = \frac{v}{f_2} = \frac{340\text{ m/s}}{500\text{ Hz}} = 0.68\text{ m}

Because wave speed is constant, an increase in frequency causes an inversely proportional decrease in wavelength.

Key Concept

Inverse relationship between frequency and wavelength in a constant medium (

v = f\lambda

)

Estimated Time:1m 0s

Question 3Question →

Understanding magnetic behaviors and electromagnetic interactions is fundamental in physical science. Match each magnetic concept on the left with its correct scientific description on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Ferromagnetic substance matches the material strongly attracted to magnets and easily magnetized; Magnetic domain matches the microscopic region where atomic magnetic fields are aligned; Magnetic field lines match the lines of force mapping direction and strength from north to south; and Electromagnetic induction matches the process of generating an electric current via a changing magnetic field.

Each physical concept is paired with its precise scientific description: ferromagnetic substances describe materials like iron and nickel that exhibit strong magnetic attraction; magnetic domains are the microscopic aligned clusters of atomic dipoles; magnetic field lines map the invisible field geometry from north to south; and electromagnetic induction refers to current generation induced by a changing magnetic environment.

Step-by-Step Solution

1

Identify the definition of a ferromagnetic substance

Matches the description of a material such as iron or nickel that is strongly attracted to magnets and can be magnetized

Ferromagnetism is the basic mechanism by which certain materials form permanent magnets or are attracted to magnets.

2

Identify the definition of a magnetic domain

Matches the description of a microscopic region within a solid where atomic magnetic fields are aligned

Domains are localized zones of uniform magnetic orientation within ferromagnetic materials.

3

Identify the definition of magnetic field lines

Matches the description of continuous lines of force emerging from north and entering south to indicate direction and strength

Field lines visually communicate the direction of the magnetic force and its magnitude through line spacing.

4

Identify the definition of electromagnetic induction

Matches the description of the process of generating an electric current in a conductor via a changing magnetic field

Relative movement between a magnetic field and a conductor produces an induced current.

Key Concept

Core concepts of magnetism, magnetic domains, field mapping, and electromagnetic induction

Estimated Time:1m 0s

Question 4Question →

An electrical circuit in an automated test bench connects a $24\text{ V}$ direct-current power supply to two $12\,\Omega$ heating elements arranged in parallel. What is the total electric current delivered by the power supply to the entire circuit?

1\text{ A}

4\text{ A}

2\text{ A}

8\text{ A}

Show answer & explanation

Answer: $4\text{ A}$

Answer

4\text{ A}

In a parallel circuit with two identical

12\,\Omega

loads, the total equivalent resistance is halved to

6\,\Omega

. By Ohm's law (

I = \frac{V}{R}

), the total current drawn from the

24\text{ V}

source is

\frac{24\text{ V}}{6\,\Omega} = 4\text{ A}

. Alternatively, each branch draws

\frac{24\text{ V}}{12\,\Omega} = 2\text{ A}

, yielding a total current of

2\text{ A} + 2\text{ A} = 4\text{ A}

.

Step-by-Step Solution

1

Calculate the equivalent resistance of the two identical resistors connected in parallel.

R_{\text{eq}} = \frac{12\,\Omega}{2} = 6\,\Omega

When identical resistors are in parallel, the equivalent resistance equals the resistance of one branch divided by the total number of branches.

2

Apply Ohm's law (

I = \frac{V}{R_{\text{eq}}}

) using the total source voltage and equivalent resistance.

I_{\text{total}} = \frac{24\text{ V}}{6\,\Omega} = 4\text{ A}

Ohm's law defines the relationship between total circuit voltage, equivalent resistance, and total current.

Key Concept

Parallel circuit resistance and Ohm's law

Estimated Time:1m 0s

Question 5Question →

A ceramic space heater is connected to a standard $120\text{ V}$ electrical outlet. If the heating element has an internal resistance of $15\,\Omega$ , what is the electric current flowing through the circuit, in amperes ( $\text{A}$ )?

Show answer & explanation

Answer: 8

Answer

8 A

According to Ohm's Law (

V = IR

), the electric current (

I

) flowing through a circuit is found by dividing the potential difference (

V

) by the resistance (

R

). Dividing

120\text{ V}

by

15\,\Omega

gives an electric current of

8\text{ A}

.

Step-by-Step Solution

1

Identify the given electrical values from the problem statement.

Voltage

V = 120\text{ V}

and resistance

R = 15\,\Omega

.

Determining known quantities is required to choose the appropriate formula.

2

State Ohm's Law and isolate current (

I

).

I = \frac{V}{R}

Ohm's Law governs the relationship between potential difference, current, and resistance in an electrical circuit.

3

Divide voltage by resistance to calculate the current in amperes.

I = \frac{120\text{ V}}{15\,\Omega} = 8\text{ A}

Carrying out the arithmetic yields the resulting current in amperes.

Key Concept

Ohm's Law (

V = IR

) defines the relationship among voltage, current, and resistance, where current is directly proportional to voltage and inversely proportional to resistance.

Estimated Time:1m 0s

Question 6Question →

An emergency backup lighting system connects three identical $15\,\Omega$ indicator lamps in series across a $45\text{ V}$ direct-current power source. What is the electric current flowing through each lamp?

0.33\text{ A}

3.0\text{ A}

1.0\text{ A}

9.0\text{ A}

Show answer & explanation

Answer: $1.0\text{ A}$

Answer

1.0\text{ A}

In a series circuit, the total electrical resistance is the sum of all individual resistances in the path:

R_{\text{total}} = 15\,\Omega + 15\,\Omega + 15\,\Omega = 45\,\Omega

. Applying Ohm's law (

I = \frac{V}{R}

), the current drawn from the

45\text{ V}

source is

I = \frac{45\text{ V}}{45\,\Omega} = 1.0\text{ A}

. In any series circuit, the electric current is identical at every point, meaning exactly

1.0\text{ A}

flows through each lamp.

Step-by-Step Solution

1

Calculate the total equivalent resistance of the series circuit.

R_{\text{total}} = 15\,\Omega + 15\,\Omega + 15\,\Omega = 45\,\Omega

In a series circuit, the total electrical resistance equals the direct sum of all individual resistances.

2

Apply Ohm's law to determine the total circuit current.

I = \frac{V}{R_{\text{total}}} = \frac{45\text{ V}}{45\,\Omega} = 1.0\text{ A}

Current is calculated by dividing total source voltage by the total resistance of the circuit.

3

Determine the current flowing through each individual lamp.

I_{\text{lamp}} = 1.0\text{ A}

Because there is only one continuous path for electrical charge in a series circuit, the current is uniform through all components.

Key Concept

Ohm's law and total resistance in series circuits

Estimated Time:1m 0s

Question 7Question →

Electrical circuits and power distribution systems utilize specialized components to regulate, convert, and protect electrical energy. Which functional description correctly matches each electrical component?

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct pairings match Fuse with interrupting excessive current by melting a sacrificial strip, Transformer with altering alternating-current voltage levels through electromagnetic induction, Capacitor with storing separated electric charge across an insulating dielectric layer, and Diode with restricting current flow primarily to a single direction.

Each component is correctly paired with its defining physical mechanism: a fuse provides overcurrent protection by melting its internal element; a transformer modulates AC voltage via mutual electromagnetic induction; a capacitor accumulates electrostatic charge across separated plates; and a diode rectifies or guides current in a single direction.

Step-by-Step Solution

1

Identify the protective mechanism of a fuse.

A fuse contains a thin wire designed to melt under overcurrent conditions, matching the description of interrupting excessive current by melting a sacrificial strip.

Fuses protect wiring and equipment from dangerous current overloads and short circuits.

2

Identify the electromagnetic function of a transformer.

A transformer transfers energy between AC circuits through mutual magnetic flux, matching the description of altering AC voltage levels through electromagnetic induction.

Transformers rely on changing magnetic fields produced by alternating current to induce voltage across windings.

3

Identify the electrostatic storage mechanism of a capacitor.

A capacitor holds electrostatic charge on opposing plates separated by a dielectric, matching the description of accumulating and storing separated electric charge.

Capacitors maintain potential difference by holding static charge rather than dissipating or converting it.

4

Identify the unidirectional conducting property of a diode.

A diode conducts forward-bias current while blocking reverse-bias current, matching the description of restricting current flow to a single direction.

Diodes are fundamental semiconductor components used in rectification and polarity protection.

Key Concept

Functional characteristics and operating principles of fundamental electrical circuit components

Estimated Time:1m 0s

Question 8Question →

A remote weather-monitoring station is powered by a $36\text{ V}$ direct-current solar battery bank. Two identical communication transmitters are connected in parallel across the power terminals. If the monitoring station draws a total current of $4\text{ A}$ when both transmitters are operating simultaneously, what is the electrical resistance of each individual transmitter?

9\,\Omega

4.5\,\Omega

18\,\Omega

180\,\Omega

Show answer & explanation

Answer: $18\,\Omega$

Answer

The electrical resistance of each individual transmitter is

18\,\Omega

.

In a parallel circuit, each identical branch draws an equal share of the total current. With a total current of

4\text{ A}

split evenly across two identical paths, each transmitter draws

2\text{ A}

. Applying Ohm's law (

R = \frac{V}{I}

) across one branch with the full

36\text{ V}

potential difference yields

R = \frac{36\text{ V}}{2\text{ A}} = 18\,\Omega

.

Step-by-Step Solution

1

Calculate the total equivalent resistance of the parallel circuit using Ohm's Law.

R_{\text{eq}} = \frac{V}{I_{\text{total}}} = \frac{36\text{ V}}{4\text{ A}} = 9\,\Omega

The total resistance of the entire circuit relates the total supply voltage to the total current drawn from the battery bank.

2

Determine the resistance of each individual transmitter from the parallel combination formula.

\frac{1}{R_{\text{eq}}} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R} \implies R = 2 \times R_{\text{eq}} = 2 \times 9\,\Omega = 18\,\Omega

When two identical resistors are connected in parallel, their equivalent resistance is equal to half the resistance of a single component.

Key Concept

Ohm's law and equivalent resistance in parallel circuits

Alternative Method

Determine the current per branch directly: because the two transmitters are identical and in parallel across the

36\text{ V}

source, each receives the full supply voltage and carries half the total current (

I_{\text{branch}} = \frac{4\text{ A}}{2} = 2\text{ A}

). Then apply Ohm's law directly to a single branch:

R = \frac{V}{I_{\text{branch}}} = \frac{36\text{ V}}{2\text{ A}} = 18\,\Omega

.

Estimated Time:1m 0s

Question 9Question →

A workshop exhaust fan is connected to a $120\text{ V}$ power supply and consumes $480\text{ W}$ of electric power during normal operation. What is the effective electrical resistance of the fan motor, in ohms ( $\Omega$ )?

Show answer & explanation

Answer: 30

Answer

The effective electrical resistance of the fan motor is

30\,\Omega

.

To find the resistance from voltage and power, determine the current using

I = \frac{P}{V} = \frac{480\text{ W}}{120\text{ V}} = 4\text{ A}

, then use Ohm's law

R = \frac{V}{I} = \frac{120\text{ V}}{4\text{ A}} = 30\,\Omega

. Alternatively, using

R = \frac{V^2}{P}

yields

\frac{120^2}{480} = \frac{14400}{480} = 30\,\Omega

.

Step-by-Step Solution

1

Calculate the electric current flowing through the fan motor using the electrical power formula

P = V \times I

.

I = \frac{P}{V} = \frac{480\text{ W}}{120\text{ V}} = 4\text{ A}

Electric power equals the product of voltage and current, so dividing total wattage by applied voltage determines circuit current.

2

Calculate the resistance using Ohm's law rearranged as

R = \frac{V}{I}

.

R = \frac{120\text{ V}}{4\text{ A}} = 30\,\Omega

Resistance represents the opposition to current flow and is found by dividing the applied voltage by the circuit current.

Key Concept

Relationship between electrical power (

P = IV

) and Ohm's law (

V = IR

)

Estimated Time:1m 0s

Question 10Question →

In an industrial facility, three identical light fixtures are connected in parallel across a constant $120\text{ V}$ electrical line. If one of the light fixtures burns out and creates an open circuit in its branch, what will happen to the remaining light fixtures and the total current drawn from the line?

All remaining fixtures go out immediately, and the total current drawn from the line drops to zero.

The remaining fixtures stay lit at the same brightness, and the total current drawn from the line decreases.

The remaining fixtures glow noticeably brighter, and the total current drawn from the line increases.

The remaining fixtures become dimmer, while the total current drawn from the line remains unchanged.

Show answer & explanation

Answer: The remaining fixtures stay lit at the same brightness, and the total current drawn from the line decreases.

Answer

The remaining fixtures stay lit at the same brightness, and the total current drawn from the line decreases.

In a parallel circuit, each device is connected across the full source voltage independently. When one fixture burns out, the voltage across the remaining fixtures remains at

120\text{ V}

, so their current and brightness stay the same. However, because the total current is the sum of the branch currents (

I_{\text{total}} = I_1 + I_2 + I_3

), losing one branch reduces the total current supplied by the line from three branch currents down to two.

Step-by-Step Solution

1

Analyze voltage across individual branches in a parallel circuit

Each remaining fixture continues to experience the full

120\text{ V}

line voltage.

In a parallel circuit, every branch is connected directly across the power source, so removing or opening one branch does not alter the voltage applied to the others.

2

Determine current and power dissipation for each remaining fixture

Individual current

I = \frac{V}{R}

and power

P = \frac{V^2}{R}

remain constant, keeping brightness unchanged.

Since both the resistance of each remaining fixture and the supply voltage remain unchanged, the power output of each active lamp does not change.

3

Calculate the effect on total circuit current

Total current drops from

I_{\text{total}} = 3I_{\text{branch}}

to

I_{\text{total}} = 2I_{\text{branch}}

.

Total current in a parallel circuit is the sum of the individual branch currents (

I_{\text{total}} = I_1 + I_2 + I_3

). When one branch opens, its current drops to zero, reducing the total current drawn from the supply.

Key Concept

Parallel Circuit Branch Independence and Current Summation

Estimated Time:1m 0s

Question 11Question →

In the analysis of direct-current electrical circuits, fundamental physical quantities define how electrical energy is stored, transported, and dissipated. Match each electrical quantity on the left with its correct physical definition on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Electric Current matches 'The rate at which electric charge flows through a cross-sectional area of a conductor over time'; Voltage (Electric Potential Difference) matches 'The amount of electric potential energy delivered or work done per unit of electric charge'; Electrical Resistance matches 'The measure of a material's opposition to the passage of electric charge'; Electrical Power matches 'The rate at which electrical energy is transferred, converted, or dissipated per unit of time'.

Each term corresponds directly to its foundational physical definition in electromagnetism: Electric Current is the rate of charge flow (

I = \frac{\Delta Q}{\Delta t}

), Voltage is the work/energy per unit charge (

V = \frac{W}{Q}

), Resistance is the opposition to charge movement (

R = \frac{V}{I}

), and Electrical Power is the time rate of total energy transfer (

P = VI

).

Step-by-Step Solution

1

Determine the physical definition of Electric Current.

Electric current is the flow of electric charge per unit time (

I = \frac{\Delta Q}{\Delta t}

), which matches 'The rate at which electric charge flows through a cross-sectional area of a conductor over time'.

Current measures how many coulombs of charge pass through a point each second.

2

Determine the physical definition of Voltage (Electric Potential Difference).

Voltage is the potential energy difference per unit charge (

V = \frac{W}{Q}

), which matches 'The amount of electric potential energy delivered or work done per unit of electric charge'.

Voltage represents the electrical 'push' or work done to move a unit charge between two points.

3

Determine the physical definition of Electrical Resistance.

Resistance describes the opposition encountered by flowing charge (

R = \frac{V}{I}

), which matches 'The measure of a material's opposition to the passage of electric charge'.

Resistance impedes electric current and creates a potential drop across a circuit component.

4

Determine the physical definition of Electrical Power.

Electrical power is the rate of energy transformation or consumption (

P = \frac{\Delta E}{\Delta t} = VI

), which matches 'The rate at which electrical energy is transferred, converted, or dissipated per unit of time'.

Power quantifies how rapidly electrical potential energy is converted into thermal energy, light, or mechanical work.

Key Concept

Fundamental electrical circuit quantities, their standard physical definitions, and underlying unit relationships

Estimated Time:1m 0s

Question 12Question →

A test car travels along a flat, circular track at a constant speed of $20\text{ m/s}$ . Which of the following statements correctly describes the velocity and acceleration of the car?

The velocity is constant because the speed does not change, meaning the car experiences zero acceleration.

The acceleration is zero because the vehicle's downward gravitational weight is fully balanced by the normal force from the road surface.

The velocity is continuously changing because its direction of motion changes, producing an acceleration directed toward the center of the track.

The velocity remains scalar because the distance units of the circular path remain constant over time.

Show answer & explanation

Answer: The velocity is continuously changing because its direction of motion changes, producing an acceleration directed toward the center of the track.

Answer

The velocity is continuously changing because its direction of motion changes, producing an acceleration directed toward the center of the track.

Velocity is a vector quantity defined by both speed and direction of travel. When an object moves along a circular path at a constant speed, its direction changes at every instant. Because velocity changes whenever direction changes, the object undergoes centripetal acceleration directed radially inward toward the center of the circle.

Step-by-Step Solution

1

Distinguish between the physical definitions of speed and velocity.

Speed (

20\text{ m/s}

) is a scalar representing magnitude, while velocity is a vector containing both magnitude and direction.

Clarifying vector vs. scalar quantities is required to evaluate motion along a curved trajectory.

2

Analyze the car's direction of travel on the circular track.

As the car follows the curve, the tangent direction of travel continuously turns.

A change in direction constitutes a change in the velocity vector, even when speed remains constant.

3

Determine the resulting acceleration.

Acceleration is the rate of change of velocity (

a = \Delta v / \Delta t

), directed inward toward the center (centripetal acceleration).

An unbalanced inward force is required to alter direction, creating non-zero acceleration.

Key Concept

Vector nature of velocity and centripetal acceleration in circular motion

Estimated Time:1m 0s

Question 13Question →

Four mobile systems are evaluated during performance trials on a flat testing course. Arrange the systems in order of their kinetic energy, from least to greatest.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

From least to greatest kinetic energy: the

500\text{ kg}

cargo transport (

4{}000\text{ J}

), the

10\text{ kg}

automated inspection rover (

4{}500\text{ J}

), the

40\text{ kg}

tracked reconnaissance unit (

8{}000\text{ J}

), and the

2\text{ kg}

calibration projectile (

10{}000\text{ J}

).

Applying the kinetic energy formula

KE = \frac{1}{2}mv^2

to each system yields

4{}000\text{ J}

for the

500\text{ kg}

transport at

4\text{ m/s}

,

4{}500\text{ J}

for the

10\text{ kg}

rover at

30\text{ m/s}

,

8{}000\text{ J}

for the

40\text{ kg}

unit at

20\text{ m/s}

, and

10{}000\text{ J}

for the

2\text{ kg}

projectile at

100\text{ m/s}

. Arranging these values from smallest to largest produces the correct sequence.

Step-by-Step Solution

1

Identify the formula for kinetic energy.

KE = \frac{1}{2}mv^2

, where

m

is mass in kilograms and

v

is velocity in meters per second.

Kinetic energy is directly proportional to mass and proportional to the square of velocity.

2

Calculate the kinetic energy for each of the four systems.

Cargo transport:

\frac{1}{2}(500)(4^2) = 250 \times 16 = 4{}000\text{ J}

; Inspection rover:

\frac{1}{2}(10)(30^2) = 5 \times 900 = 4{}500\text{ J}

; Reconnaissance unit:

\frac{1}{2}(40)(20^2) = 20 \times 400 = 8{}000\text{ J}

; Calibration projectile:

\frac{1}{2}(2)(100^2) = 1 \times 10{}000 = 10{}000\text{ J}

.

Quantitative values allow direct comparison across all systems.

3

Arrange the resulting energy values in ascending sequence.

4{}000\text{ J} < 4{}500\text{ J} < 8{}000\text{ J} < 10{}000\text{ J}

.

Orders the systems from least kinetic energy to greatest kinetic energy as required.

Key Concept

Kinetic energy is calculated as

KE = \frac{1}{2}mv^2

, meaning velocity has a quadratic effect compared to the linear effect of mass.

Estimated Time:1m 30s

Question 14Question →

A radar operator tracks a reconnaissance aircraft traveling due east at a constant rate of $450\text{ knots}$ . Which of the following physical quantities does this measurement represent?

Speed, because any rate of travel across a distance is a scalar value

Velocity, because it specifies both a magnitude and a direction of motion

Acceleration, because standard navigation units always denote a rate of change

Weight, because aircraft propulsion depends directly on gravitational load

Show answer & explanation

Answer: Velocity, because it specifies both a magnitude and a direction of motion

Answer

Velocity, because the measurement includes both a numerical magnitude and a directional component.

Velocity is a vector quantity that requires both a magnitude (speed) and an explicit directional heading. Because the radar measurement provides both the rate (

450\text{ knots}

) and the direction ('due east'), it represents velocity.

Step-by-Step Solution

1

Analyze the given physical measurement components

The measurement contains a numerical rate (

450\text{ knots}

) and a compass direction (due east).

Determining the correct kinematic quantity requires identifying whether direction is specified alongside magnitude.

2

Distinguish between scalar and vector quantities

Speed is scalar (magnitude only), while velocity is vector (magnitude plus direction).

Since both speed and direction are explicitly stated, the measurement represents velocity.

Key Concept

Difference between scalar speed and vector velocity in kinematics

Estimated Time:40s

Question 15Question →

Consider the chemical equation for the formation of ammonia from its constituent elements: $\text{N}_2 + \underline{\quad}\text{H}_2 \rightarrow 2\text{NH}_3$ . What missing coefficient and reaction type correctly complete the statement?

Fill in the blanks below

In the chemical equation $\text{N}_2 + \text{H}_2 \rightarrow 2\text{NH}_3$, the coefficient required to balance the hydrogen atoms is , and because two distinct reactants combine to yield a single compound, this process is classified as a reaction.

Show answer & explanation

Answer

The missing coefficient is 3 and the reaction is classified as a synthesis (or combination) reaction.

On the product side,

2\text{NH}_3

contains 2 nitrogen atoms and 6 hydrogen atoms. On the reactant side,

\text{N}_2

accounts for the 2 nitrogen atoms, so 3 molecules of

\text{H}_2

(

3 \times 2 = 6

atoms) are required to balance the hydrogen. Furthermore, because two separate elemental substances combine to form a single compound, the reaction represents a synthesis (combination) reaction.

Step-by-Step Solution

1

Count the number of hydrogen atoms in the product side of the equation.

The product side contains

2\text{NH}_3

, which has

2 \times 3 = 6

hydrogen atoms.

According to the law of conservation of mass, the total number of atoms of each element must be equal on both sides of the equation.

2

Determine the coefficient for the reactant

\text{H}_2

needed to provide 6 hydrogen atoms.

Since each diatomic hydrogen molecule (

\text{H}_2

) contains 2 atoms, dividing 6 by 2 yields a coefficient of 3.

Setting the coefficient of

\text{H}_2

to 3 balances the hydrogen atoms (

3 \times 2 = 6

) while nitrogen is already balanced (

2 = 2

).

3

Identify the reaction type based on the reactants and products.

Two elemental reactants (

\text{N}_2

and

\text{H}_2

) combine directly to form a single chemical compound (

\text{NH}_3

).

A chemical reaction in which two or more simple substances combine to form a single complex substance is defined as a synthesis (or combination) reaction.

Key Concept

Balancing chemical equations by conserving atoms and classifying reaction types (synthesis/combination).

Estimated Time:1m 0s

Question 16Question →

A transport vehicle with a mass of $2{}000\text{ kg}$ travels along a straight, level road at a constant velocity of $20\text{ m/s}$ . The driver applies the brakes, causing the vehicle to decelerate uniformly to a complete stop over a distance of $40\text{ m}$ . What is the magnitude of the net horizontal braking force acting on the vehicle?

1{}000\text{ N}

10{}000\text{ N}

19{}600\text{ N}

100{}000\text{ N}

Show answer & explanation

Answer: $10{}000\text{ N}$

Answer

The magnitude of the net horizontal braking force is

10{}000\text{ N}

.

The magnitude of the acceleration is determined by

v_f^2 = v_i^2 + 2ad

, yielding

a = 5\text{ m/s}^2

. According to Newton's Second Law (

F = ma

), multiplying the mass of

2{}000\text{ kg}

by

5\text{ m/s}^2

results in a net braking force of

10{}000\text{ N}

.

Step-by-Step Solution

1

Calculate the magnitude of uniform acceleration using the kinematic equation relating velocity, acceleration, and displacement:

v_f^2 = v_i^2 + 2a\Delta x

.

0^2 = (20\text{ m/s})^2 + 2a(40\text{ m}) \implies 0 = 400 + 80a \implies a = -5\text{ m/s}^2

. The magnitude of acceleration is

5\text{ m/s}^2

.

The acceleration must be found from the known initial speed (

20\text{ m/s}

), final speed (

0\text{ m/s}

), and stopping distance (

40\text{ m}

).

2

Apply Newton's Second Law of Motion (

F_{\text{net}} = ma

) to find the magnitude of the net horizontal braking force.

F_{\text{net}} = (2{}000\text{ kg})(5\text{ m/s}^2) = 10{}000\text{ N}

.

The net force required to decelerate the mass is the product of mass and acceleration.

Key Concept

Kinematic equations for uniform deceleration and Newton's Second Law of Motion (

F = ma

)

Alternative Method

Find the average velocity

v_{\text{avg}} = \frac{v_i + v_f}{2} = \frac{20 + 0}{2} = 10\text{ m/s}

. The stopping time is

t = \frac{d}{v_{\text{avg}}} = \frac{40}{10} = 4\text{ s}

. Acceleration is

a = \frac{\Delta v}{t} = \frac{20}{4} = 5\text{ m/s}^2

, giving

F = ma = 2{}000 \times 5 = 10{}000\text{ N}

.

Estimated Time:1m 30s

Question 17Question →

A motorized winch pulls an $80\text{ kg}$ cargo pallet horizontally from rest across a concrete loading platform. The winch exerts a constant horizontal pulling force of $440\text{ N}$ , while a constant kinetic friction force of $120\text{ N}$ opposes the motion. What is the final speed of the pallet in meters per second ( $\text{m/s}$ ) after being pulled continuously for $5\text{ seconds}$ ?

Show answer & explanation

Answer: 20

Answer

20\text{ m/s}

The correct speed is

20\text{ m/s}

. By finding the net unbalanced force (

440\text{ N} - 120\text{ N} = 320\text{ N}

), the acceleration of the

80\text{ kg}

pallet is calculated as

a = 320 / 80 = 4\text{ m/s}^2

. Multiplying this constant acceleration by the elapsed time of

5\text{ s}

yields the final speed of

20\text{ m/s}

.

Step-by-Step Solution

1

Determine the net horizontal force acting on the cargo pallet by subtracting the opposing friction force from the applied pulling force.

F_{\text{net}} = 440\text{ N} - 120\text{ N} = 320\text{ N}

According to Newton's laws of motion, acceleration is produced only by the unbalanced net force acting on the mass.

2

Calculate the constant horizontal acceleration using Newton's second law of motion (

a = \frac{F_{\text{net}}}{m}

).

a = \frac{320\text{ N}}{80\text{ kg}} = 4\text{ m/s}^2

The acceleration of an object is directly proportional to the net force and inversely proportional to its mass.

3

Compute the final speed after

5\text{ seconds}

using the kinematic velocity-time relationship (

v = v_0 + at

) with an initial speed of

0\text{ m/s}

.

v = 0\text{ m/s} + (4\text{ m/s}^2)(5\text{ s}) = 20\text{ m/s}

For an object undergoing constant acceleration from rest, final velocity is the product of acceleration and elapsed time.

Key Concept

Newton's Second Law combined with linear kinematics under constant net force

Estimated Time:1m 30s

Question 18Question →

A pendulum bob is pulled to its highest point and released from rest. As the bob swings downward toward the lowest point of its path, which of the following energy transformations occurs?

Kinetic energy is converted into gravitational potential energy.

Gravitational potential energy is converted into kinetic energy.

Chemical energy is converted into thermal energy.

Gravitational potential energy and kinetic energy both decrease simultaneously.

Show answer & explanation

Answer: Gravitational potential energy is converted into kinetic energy.

Answer

Gravitational potential energy is converted into kinetic energy.

At the highest point of its swing, the pendulum bob possesses maximum gravitational potential energy due to its position and zero kinetic energy because its velocity is zero. As it falls downward toward the lowest point, gravity accelerates the bob, converting its stored gravitational potential energy into kinetic energy.

Step-by-Step Solution

1

Identify the initial energy state at the highest point of the swing.

At the peak, the pendulum bob has maximum gravitational potential energy (

PE = mgh

) and zero kinetic energy (

KE = 0

) because it is momentarily stationary.

Gravitational potential energy depends on the height of the object above its reference level.

2

Analyze the energy change as the bob descends toward the lowest point.

The bob loses height, which decreases its gravitational potential energy, and accelerates downward, increasing its kinetic energy (

KE = \frac{1}{2}mv^2

).

By the law of conservation of mechanical energy, the lost potential energy transforms directly into kinetic energy.

Key Concept

Conservation and Transformation of Mechanical Energy

Estimated Time:45s

Question 19Question →

A roller coaster car is released from rest at the top of a hill and coasts without friction along a track. Place the following track locations in order from LEAST kinetic energy to GREATEST kinetic energy.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

Starting crest (highest elevation) → Halfway down the slope → Near the bottom of the incline → Lowest point of the track (ground level)

By the conservation of energy, gravitational potential energy is continuously converted into kinetic energy as the car moves downhill. Since the car starts from rest at the highest elevation, its initial kinetic energy is zero. As it descends, its speed increases, reaching maximum kinetic energy at the lowest point of the track.

Step-by-Step Solution

1

Identify the initial energy state and energy transformation mechanism

At rest at the highest point, kinetic energy is zero (

E_k = 0

) and potential energy is at its maximum.

Kinetic energy depends on speed (

E_k = \frac{1}{2}mv^2

), so an object at rest has zero kinetic energy.

2

Apply the law of conservation of mechanical energy as the car descends

As elevation decreases, gravitational potential energy is converted into kinetic energy, increasing the speed of the car.

In a frictionless system, total mechanical energy is conserved (

E_{total} = E_p + E_k

).

3

Rank the positions from lowest to highest kinetic energy based on elevation

Elevation from highest to lowest directly corresponds to kinetic energy from least to greatest: crest (

0\text{ J}

) < halfway down < near bottom < lowest point (maximum).

Lower elevation yields lower potential energy and higher kinetic energy.

Key Concept

Conservation of Mechanical Energy and Potential-to-Kinetic Energy Transformation

Estimated Time:45s

Question 20Question →

A roller coaster cart begins from rest at the top of a track with $50{}000\text{ J}$ of gravitational potential energy. Assuming no energy is lost to friction, what is the cart's kinetic energy when its potential energy decreases to $15{}000\text{ J}$ ?

15{}000\text{ J}

50{}000\text{ J}

35{}000\text{ J}

65{}000\text{ J}

Show answer & explanation

Answer: $35{}000\text{ J}$

Answer

35{}000\text{ J}

According to the Law of Conservation of Energy, the total mechanical energy in a frictionless system remains constant. Since the cart starts with

50{}000\text{ J}

of potential energy and zero kinetic energy, the total energy is

50{}000\text{ J}

. When potential energy drops to

15{}000\text{ J}

, the lost potential energy (

50{}000\text{ J} - 15{}000\text{ J} = 35{}000\text{ J}

) is entirely converted into kinetic energy.

Step-by-Step Solution

1

Determine the total initial mechanical energy of the cart.

E_{\text{total}} = 50{}000\text{ J}

Since the cart starts from rest, its initial kinetic energy is zero, making total mechanical energy equal to initial potential energy.

2

Apply the Law of Conservation of Mechanical Energy at the lower height.

E_{\text{total}} = PE + KE \implies 50{}000\text{ J} = 15{}000\text{ J} + KE

In a frictionless system, the sum of kinetic and potential energy remains constant at all points.

3

Subtract the remaining potential energy from the total mechanical energy to solve for kinetic energy.

KE = 50{}000\text{ J} - 15{}000\text{ J} = 35{}000\text{ J}

The decrease in gravitational potential energy directly converts into an equal increase in kinetic energy.

Key Concept

Conservation of Mechanical Energy

Estimated Time:1m 0s

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