Mechanics and Motion Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

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 2Question →

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 3Question →

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 4Question →

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 5Question →

A lunar exploration probe has a mass of $60\text{ kg}$ on Earth, where gravitational acceleration is $9.8\text{ m/s}^2$ . The probe is transported to the Moon, where gravitational acceleration is $1.6\text{ m/s}^2$ . A thruster applies a constant horizontal net force of $180\text{ N}$ to propel the probe along a frictionless test surface. What is the mass of the probe on the Moon, and what is the magnitude of its horizontal acceleration?

The mass is

10\text{ kg}

, and the acceleration is

18.0\text{ m/s}^2

.

The mass is

96\text{ kg}

, and the acceleration is

1.88\text{ m/s}^2

.

The mass is

60\text{ kg}

, and the acceleration is

3.0\text{ m/s}^2

.

The mass is

60\text{ kg}

, and the acceleration is

1.4\text{ m/s}^2

.

Show answer & explanation

Answer: The mass is $60\text{ kg}$ , and the acceleration is $3.0\text{ m/s}^2$ .

Answer

The probe's mass on the Moon is

60\text{ kg}

, and its horizontal acceleration is

3.0\text{ m/s}^2

.

Mass is a fundamental scalar quantity that measures an object's inertia (resistance to acceleration) and remains constant regardless of the gravitational environment. On the Moon, the probe retains its full mass of

60\text{ kg}

. By Newton's second law of motion, the horizontal acceleration is determined by dividing the net horizontal force by the mass:

a = \frac{F}{m} = \frac{180\text{ N}}{60\text{ kg}} = 3.0\text{ m/s}^2

.

Step-by-Step Solution

1

Determine the mass of the probe on the Moon

The mass remains

60\text{ kg}

.

Mass measures the amount of matter in an object and its inertia; it does not change with the local gravitational field strength.

2

Apply Newton's second law of motion (

F_{\text{net}} = ma

) to find horizontal acceleration

a = \frac{F_{\text{net}}}{m} = \frac{180\text{ N}}{60\text{ kg}} = 3.0\text{ m/s}^2

The horizontal thrust provides the net horizontal force on a frictionless surface, accelerating the object's mass.

Key Concept

Mass is an invariant intrinsic property representing inertia, whereas acceleration depends solely on the net applied force divided by that mass according to Newton's Second Law (

F = ma

).

Estimated Time:1m 15s

Question 6Question →

In Newtonian mechanics and kinematics, distinct physical parameters govern the translational and curved motion of bodies. Match each mechanical quantity with its precise physical definition and governing mathematical relationship.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Impulse matches the force applied over a time interval causing a change in momentum (

J = F_{\text{avg}} \Delta t

); Centripetal Acceleration matches the inward rate of directional velocity change on a curve (

a_c = \frac{v^2}{r}

); Kinetic Friction Force matches the dissipative sliding resistance proportional to normal force (

f_k = \mu_k F_N

); and Instantaneous Velocity matches the time rate of change of position (

v = \frac{d\mathbf{r}}{dt}

).

Each mechanics quantity matches its exact standard definition and mathematical formula: Impulse represents force applied across time; Centripetal Acceleration measures inward radial turning acceleration; Kinetic Friction Force calculates contact resistance against sliding; and Instantaneous Velocity specifies the instantaneous vector rate of positional change.

Step-by-Step Solution

1

Identify the definition and formula for Impulse

Impulse equals

F_{\text{avg}} \Delta t = \Delta p

, representing force integrated over time.

According to the impulse-momentum theorem, impulse measures the total momentum transfer delivered by a force over an elapsed time.

2

Identify the definition and formula for Centripetal Acceleration

Centripetal acceleration equals

a_c = \frac{v^2}{r}

, oriented radially inward.

In circular and curvilinear dynamics, inward acceleration is required to change velocity direction without necessarily changing tangential speed.

3

Identify the definition and formula for Kinetic Friction Force

Kinetic friction force equals

f_k = \mu_k F_N

, opposing relative sliding.

Amontons' and Coulomb's laws of friction state that kinetic friction depends directly on the normal force pressing two surfaces together.

4

Identify the definition and formula for Instantaneous Velocity

Instantaneous velocity equals

v = \frac{d\mathbf{r}}{dt}

, establishing magnitude and directional vector heading.

Velocity is the first derivative of position with respect to time, distinguishing it from scalar speed by including direction.

Key Concept

Fundamental kinematic definitions and dynamic force-motion relationships in Newtonian mechanics.

Estimated Time:1m 30s

Question 7Question →

In the study of classical mechanics, fundamental terms describe the motion of objects and their response to forces. Match each mechanics term on the left with its correct scientific definition on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Velocity corresponds to the rate of change of position in a specified direction; Acceleration corresponds to the rate at which velocity changes over time; Inertia corresponds to an object's resistance to changes in its state of motion; and Momentum corresponds to the product of an object's mass and velocity.

The pairings correctly match each fundamental physical term to its scientific definition: Velocity is position change over time with direction; Acceleration is velocity change over time; Inertia is the intrinsic resistance of matter to motion changes; and Momentum is the product of mass and velocity.

Step-by-Step Solution

1

Define Velocity

Velocity is displacement divided by elapsed time (

v = \frac{\Delta x}{\Delta t}

), including direction.

It describes how rapidly an object changes its position in a particular direction.

2

Define Acceleration

Acceleration is the change in velocity divided by time (

a = \frac{\Delta v}{\Delta t}

).

It quantifies speeding up, slowing down, or changing direction.

3

Define Inertia

Inertia is proportional to mass and represents resistance to acceleration.

According to Newton's first law, a body maintains constant velocity unless acted upon by a net external force.

4

Define Momentum

Momentum (

p

) is calculated as mass times velocity (

p = mv

).

It represents the overall moving mass and determines the impact force needed to bring an object to rest.

Key Concept

Core kinematic and dynamic quantities in mechanics: velocity, acceleration, inertia, and momentum.

Estimated Time:45s

Question 8Question →

A model electric car accelerates uniformly along a straight track from rest to a speed of $12\text{ m/s}$ in $4\text{ seconds}$ . What is the magnitude of the car's acceleration in meters per second squared ( $\text{m/s}^2$ )?

Show answer & explanation

Answer: 3

Answer

The magnitude of the acceleration is

3\text{ m/s}^2

.

Acceleration is defined as the change in velocity divided by the time elapsed (

a = \frac{\Delta v}{t}

). Since the car accelerates from

0\text{ m/s}

to

12\text{ m/s}

in

4\text{ s}

, the acceleration is

\frac{12 - 0}{4} = 3\text{ m/s}^2

.

Step-by-Step Solution

1

Identify the given physical quantities from the problem statement

Initial velocity

v_i = 0\text{ m/s}

, final velocity

v_f = 12\text{ m/s}

, time

t = 4\text{ s}

Establishing known variables is necessary before selecting the appropriate kinematic relationship.

2

Apply the definition of constant linear acceleration:

a = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{t}

Formula set up as

a = \frac{12\text{ m/s} - 0\text{ m/s}}{4\text{ s}}

Acceleration represents the rate of change of velocity with respect to time.

3

Perform the division to compute acceleration

a = 3\text{ m/s}^2

Dividing

12

by

4

yields the constant acceleration magnitude.

Key Concept

Uniform Linear Acceleration

Alternative Method

Using the kinematic equation

v_f = v_i + at

, substitute

12 = 0 + a(4)

, which simplifies directly to

4a = 12

, yielding

a = 3\text{ m/s}^2

.

Estimated Time:45s

Question 9Question →

A $3\text{ kg}$ object moving at $20\text{ m/s}$ along a frictionless horizontal surface collides with and sticks to a stationary $7\text{ kg}$ object. Immediately after the collision, the combined mass slides onto a rough surface with a coefficient of kinetic friction of $0.3$ . Assuming the acceleration due to gravity is $10\text{ m/s}^2$ , how many meters will the combined mass slide before coming to a complete stop?

Show answer & explanation

Answer: 6

Answer

6

The problem is solved in two phases. Phase 1 is the perfectly inelastic collision, where momentum is conserved:

p_i = p_f \Rightarrow (3)(20) = (10)v

, which gives a shared velocity of

6\text{ m/s}

. Phase 2 is the sliding on a rough surface, where the only horizontal force is kinetic friction. The acceleration is

a = -\mu_k g = -(0.3)(10) = -3\text{ m/s}^2

. Finally, using the kinematic equation

v_f^2 = v_i^2 + 2ad

(where

v_f = 0

), we get

0 = 36 + 2(-3)d

, yielding

d = 6\text{ meters}

.

Step-by-Step Solution

1

Apply the law of conservation of momentum to find the velocity of the combined mass immediately after the collision.

v = 6\text{ m/s}

In a perfectly inelastic collision, momentum is conserved (

m_1v_1 + m_2v_2 = (m_1+m_2)v

). Therefore,

3(20) + 7(0) = 10v

.

2

Calculate the deceleration of the combined mass due to kinetic friction.

a = -3\text{ m/s}^2

The net force is kinetic friction (

F_k = \mu_k m g

). Using Newton's second law, acceleration

a = -F_k / m = -\mu_k g = -0.3(10)

.

3

Use kinematics to find the distance required for the mass to come to a stop.

d = 6\text{ m}

Using the time-independent kinematic equation

v_f^2 = v_i^2 + 2ad

with

v_f = 0\text{ m/s}

,

v_i = 6\text{ m/s}

, and

a = -3\text{ m/s}^2

.

Key Concept

Conservation of Momentum and Kinematics

Question 10Question →

A motorized conveyor system applies a constant horizontal net force of $80\text{ N}$ to a container, causing it to accelerate along a smooth surface at $4\text{ m/s}^2$ . What is the mass of the container?

320\text{ kg}

20\text{ kg}

20\text{ N}

0.05\text{ kg}

Show answer & explanation

Answer: $20\text{ kg}$

Answer

The mass of the container is

20\text{ kg}

.

According to Newton's second law of motion (

F = ma

), mass is equal to net force divided by acceleration (

m = \frac{F}{a}

). Dividing

80\text{ N}

by

4\text{ m/s}^2

gives

20\text{ kg}

.

Step-by-Step Solution

1

Identify the given physical quantities and the relevant equation.

Net Force

F = 80\text{ N}

, Acceleration

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

, and Newton's Second Law is

F = ma

.

Newton's second law relates net force, mass, and acceleration.

2

Rearrange the equation to solve for mass (

m

) and substitute the given values.

m = \frac{F}{a} = \frac{80\text{ N}}{4\text{ m/s}^2} = 20\text{ kg}

.

Dividing both sides of

F = ma

by

a

isolates the unknown mass

m

.

Key Concept

Newton's Second Law of Motion (

F = ma

)

Estimated Time:45s

Question 11Question →

In everyday physical interactions, distinct forces and kinematic principles govern how objects start, change, or cease their motion. Which pairs correctly match each physical observation on the left with its primary governing principle on the right?

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct pairings match the sliding toolbox with frictional force, the lurching passenger with inertia, the falling wrench with gravitational attraction, and the harder-to-stop loaded cart with momentum.

Each observation directly matches the defining characteristic of its governing principle: surface resistance causing slowing is friction, resistance to change in motion is inertia, downward acceleration is gravity, and mass-dependent difficulty in stopping a moving object is momentum.

Step-by-Step Solution

1

Analyze the cause of stopping motion for sliding surfaces.

Identify friction as the contact force resisting sliding between the toolbox and deck.

Friction opposes sliding motion parallel to contacting surfaces.

2

Examine the tendency of a passenger to keep moving forward during sudden braking.

Identify inertia as the property of matter resisting changes in velocity.

Newton's First Law explains that objects in motion stay in motion unless acted upon by a net external force.

3

Determine the downward pull on unsupported falling objects.

Identify gravity as the non-contact attractive force pulling mass downward.

Earth's gravity accelerates falling objects toward the ground at approximately

9.8\text{ m/s}^2

.

4

Evaluate why a heavier cart at equal speed is harder to bring to rest.

Identify momentum (

p = mv

) as the quantity dependent on mass and speed that dictates stopping effort.

Greater mass at the same speed yields larger momentum, requiring greater impulse to stop.

Key Concept

Fundamental mechanical principles including friction, inertia, gravity, and momentum governing the motion and interaction of objects.

Estimated Time:45s

Question 12Question →

A physicist conducts an experiment with a solid block on a perfectly frictionless horizontal track. On Earth, a constant horizontal force of $150\text{ N}$ applied to the block produces a forward acceleration of $3\text{ m/s}^2$ . If the physicist transports the exact same block and track to an exoplanet where the acceleration due to gravity is exactly one-fifth that of Earth, and applies the identical $150\text{ N}$ horizontal force, which of the following describes the block's resulting mass and forward acceleration?

The mass remains

50\text{ kg}

, and the acceleration remains

3\text{ m/s}^2

.

The mass decreases to

10\text{ kg}

, and the acceleration increases to

15\text{ m/s}^2

.

The mass remains

50\text{ kg}

, but the acceleration increases to

15\text{ m/s}^2

.

The mass decreases to

10\text{ kg}

, but the acceleration remains

3\text{ m/s}^2

.

Show answer & explanation

Answer: The mass remains $50\text{ kg}$ , and the acceleration remains $3\text{ m/s}^2$ .

Answer

The mass remains

50\text{ kg}

, and the acceleration remains

3\text{ m/s}^2

.

The block's mass is an intrinsic property and remains

50\text{ kg}

regardless of the local gravitational field. Because the track is frictionless, the object's horizontal acceleration is determined solely by the applied horizontal force and its mass (

a = F/m

). Since neither the applied force (

150\text{ N}

) nor the mass (

50\text{ kg}

) changed, the acceleration remains exactly the same at

3\text{ m/s}^2

.

Step-by-Step Solution

1

Calculate the mass of the block on Earth using Newton's second law (

F = ma

).

m = 150\text{ N} / 3\text{ m/s}^2 = 50\text{ kg}

.

Mass is the ratio of applied net force to the resulting acceleration.

2

Determine the mass of the block on the exoplanet.

The mass remains

50\text{ kg}

.

Mass is an intrinsic property of an object measuring its inertia; it does not change based on the local gravitational field.

3

Calculate the horizontal acceleration on the exoplanet.

a = F / m = 150\text{ N} / 50\text{ kg} = 3\text{ m/s}^2

.

On a frictionless horizontal surface, vertical forces (weight and normal force) do not impact horizontal motion. The only horizontal force is the

150\text{ N}

applied force, and because the mass is unchanged, the acceleration remains identical.

Key Concept

Invariance of Mass and Independence of Horizontal Inertia from Gravity

Question 13Question →

A remote-controlled toy boat with a mass of $2\text{ kg}$ accelerates across a calm pond at a rate of $3\text{ m/s}^2$ . What is the net horizontal force acting on the boat?

6\text{ kg}

6\text{ N}

1.5\text{ N}

6\text{ m/s}

Show answer & explanation

Answer: $6\text{ N}$

Answer

The net horizontal force acting on the boat is

6\text{ N}

.

Newton's second law of motion states that net force equals mass multiplied by acceleration (

F = ma

). Multiplying the mass of

2\text{ kg}

by the acceleration of

3\text{ m/s}^2

yields a net force of

6\text{ N}

.

Step-by-Step Solution

1

Identify the given values from the problem statement.

Mass

m = 2\text{ kg}

and acceleration

a = 3\text{ m/s}^2

.

Determining the known variables allows the direct application of Newton's second law of motion.

2

Apply the formula for Newton's second law of motion (

F = ma

).

F = 2\text{ kg} \times 3\text{ m/s}^2 = 6\text{ N}

.

Multiplying mass in kilograms by acceleration in meters per second squared yields force in newtons (

1\text{ N} = 1\text{ kg}\cdot\text{m/s}^2

).

Key Concept

Newton's Second Law of Motion (

F = ma

)

Estimated Time:45s

Question 14Question →

A science teacher simultaneously drops a steel hammer and a bird feather from the same height inside a sealed vacuum chamber that contains no air. Which of the following best predicts the motion of the two objects?

The hammer will hit the bottom first because an object with greater mass experiences a larger downward acceleration.

Both objects will hit the bottom at the exact same time because gravity accelerates all objects at the same rate in the absence of air resistance.

The feather will hit the bottom first because an object with less mass attains downward velocity more quickly in a vacuum.

The hammer will hit the bottom first because its weight measured in metric units causes it to reach terminal velocity sooner.

Show answer & explanation

Answer: Both objects will hit the bottom at the exact same time because gravity accelerates all objects at the same rate in the absence of air resistance.

Answer

Both objects will hit the bottom at the exact same time because gravity accelerates all objects at the same rate in the absence of air resistance.

In the absence of air resistance, the only force acting on falling objects is gravity. Although a heavier object experiences a greater gravitational pull (weight), it also has proportionally greater inertia (resistance to acceleration). As a result of

a = \frac{F}{m} = g

, all objects accelerate downward at the constant rate of approximately

9.8\text{ m/s}^2

on Earth, reaching the surface at the exact same time when released together from the same height.

Step-by-Step Solution

1

Identify the external forces acting on the objects inside the chamber.

Only the downward force of gravity acts on the objects, as air resistance is zero in a vacuum.

Recognizing the environmental conditions determines whether drag forces affect the fall.

2

Apply Newton's second law of motion (

F = ma

) to determine acceleration due to gravity.

The acceleration is calculated as

a = \frac{F_g}{m} = \frac{mg}{m} = g

.

Demonstrates that the mass

m

cancels out, proving acceleration is independent of mass.

3

Compare the arrival times of both falling objects released from the same height.

Since both start from rest with identical acceleration

g

, both take time

t = \sqrt{\frac{2h}{g}}

to reach the bottom.

Confirms that both items strike the floor simultaneously.

Key Concept

Acceleration due to gravity in free fall without air resistance

Estimated Time:45s

Question 15Question →

A $15\text{ kg}$ sled slides across a smooth ice rink at a constant velocity of $4\text{ m/s}$ . What is the magnitude of the sled's momentum in kilogram-meters per second ( $\text{kg}\cdot\text{m/s}$ )?

Show answer & explanation

Answer: 60

Answer

60 kg·m/s

Linear momentum is calculated using the formula

p = m \times v

. For an object with a mass of

15\text{ kg}

moving at

4\text{ m/s}

, the momentum is

15\text{ kg} \times 4\text{ m/s} = 60\text{ kg}\cdot\text{m/s}

.

Step-by-Step Solution

1

Identify the given mass and velocity values.

m = 15\text{ kg}

and

v = 4\text{ m/s}

Linear momentum depends directly on an object's mass and its velocity.

2

Apply the momentum formula

p = m \times v

.

p = 15\text{ kg} \times 4\text{ m/s} = 60\text{ kg}\cdot\text{m/s}

Multiplying mass by velocity calculates the magnitude of linear momentum.

Key Concept

Linear momentum is the product of an object's mass and its velocity (

p = mv

).

Estimated Time:45s

Question 16Question →

Match each fundamental physical law of mechanics to the statement that correctly describes it.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Newton's First Law pairs with the principle that an object maintains constant velocity unless acted on by an external net force; Newton's Second Law pairs with acceleration being proportional to net force and inversely proportional to mass (

F = ma

); Newton's Third Law pairs with equal and opposite action-reaction forces; Newton's Law of Universal Gravitation pairs with mutual mass-dependent attraction that weakens with distance squared.

Each mechanics law corresponds to its standard scientific definition: the First Law defines inertia (constant velocity without net force), the Second Law establishes the relationship between force, mass, and acceleration (

F = ma

), the Third Law describes equal and opposite interaction forces between bodies, and the Law of Universal Gravitation defines mutual mass attraction.

Step-by-Step Solution

1

Identify the principle governing motion when the net force is zero.

This describes inertia, which is Newton's First Law.

An object resists changes to its velocity when no net force acts on it.

2

Identify the formula and relationship linking net force, mass, and acceleration.

This corresponds to

F = ma

, which is Newton's Second Law.

Acceleration is produced when an unbalanced net force acts upon a given mass.

3

Identify the law governing force interactions between two distinct objects.

This corresponds to action-reaction pairs, which is Newton's Third Law.

Forces always act simultaneously in opposite directions on interacting bodies.

4

Identify the law describing mutual attraction between any two masses across space.

This corresponds to Newton's Law of Universal Gravitation.

Gravitational pull depends directly on the product of masses and inversely on distance squared.

Key Concept

Newton's Laws of Motion and Gravitation

Estimated Time:45s

Question 17Question →

A delivery van travels along a circular entrance ramp at a constant speed of $25\text{ mph}$ . Why is the vehicle considered to be accelerating even though the speedometer reading remains unchanged?

The van's weight decreases as gravitational pull weakens around the curve.

The speedometer records distance in miles rather than standard metric units.

The direction of travel is constantly changing, which alters the vehicle's velocity.

Speed is a vector quantity that automatically increases whenever an object turns.

Show answer & explanation

Answer: The direction of travel is constantly changing, which alters the vehicle's velocity.

Answer

The direction of travel is constantly changing, which alters the vehicle's velocity.

Acceleration is defined in physics as the rate of change of velocity over time. Because velocity is a vector quantity consisting of both speed and direction, an object traveling in a circle is continuously changing its direction. This continuous change in direction means the velocity vector is changing, which produces acceleration directed toward the center of the turn.

Step-by-Step Solution

1

Define the relationship between speed, velocity, and acceleration

Speed is a scalar quantity (magnitude only), whereas velocity is a vector quantity (both magnitude and direction). Acceleration (

a

) is the rate of change of velocity:

a = \frac{\Delta v}{\Delta t}

.

Determining whether an object is accelerating requires evaluating its velocity vector rather than just its scalar speed.

2

Analyze the motion of the vehicle on a curved path

Although the magnitude of the velocity (speed) is steady at

25\text{ mph}

, the direction of travel continuously turns along the curve.

A change in the direction of a vector constitutes a change in velocity.

3

Conclude whether acceleration occurs

Because velocity changes continuously with direction, the vehicle undergoes centripetal acceleration directed toward the center of the curve.

Any non-zero change in velocity over time confirms acceleration.

Key Concept

Velocity is a vector quantity comprising both magnitude and direction; thus, changing direction at constant speed results in acceleration.

Estimated Time:45s

Question 18Question →

A motorized winch pulls a cable, accelerating a load from rest ( $0\text{ m/s}$ ) to a final velocity of $18\text{ m/s}$ in $6\text{ seconds}$ at a constant rate. What is the acceleration of the load in meters per second squared ( $\text{m/s}^2$ )?

Show answer & explanation

Answer: 3

Answer

The acceleration of the load is

3\text{ m/s}^2

.

Acceleration is calculated by dividing the total change in velocity by the elapsed time (

a = \frac{\Delta v}{t}

). Because the load accelerates uniformly from

0\text{ m/s}

to

18\text{ m/s}

over

6\text{ s}

, the acceleration is

\frac{18\text{ m/s} - 0\text{ m/s}}{6\text{ s}} = 3\text{ m/s}^2

.

Step-by-Step Solution

1

Identify the initial velocity, final velocity, and elapsed time from the given problem.

v_i = 0\text{ m/s}

,

v_f = 18\text{ m/s}

, and

t = 6\text{ s}

These parameters are required to calculate uniform linear acceleration.

2

Set up the acceleration formula:

a = \frac{\Delta v}{t} = \frac{v_f - v_i}{t}

.

a = \frac{18 - 0}{6}

Acceleration represents the rate of change of velocity with respect to time.

3

Perform the division to compute the numerical value.

a = 3\text{ m/s}^2

Dividing

18\text{ m/s}

by

6\text{ s}

yields

3\text{ m/s}^2

.

Key Concept

Linear acceleration is defined as the change in velocity divided by the time interval over which the change occurs (

a = \frac{\Delta v}{t}

).

Estimated Time:45s

Question 19Question →

A mechanical crane lifts a cargo container with a mass of $500\text{ kg}$ vertically upward. If the crane's cable exerts a constant upward tension of $6{}400\text{ N}$ and the acceleration due to gravity is $9.8\text{ m/s}^2$ , what is the upward acceleration of the container?

12.8\text{ m/s}^2

3\text{ m/s}^2

11.8\text{ m/s}^2

0.3\text{ m/s}^2

Show answer & explanation

Answer: $3\text{ m/s}^2$

Answer

3\text{ m/s}^2

The container experiences two vertical forces: an upward tension of

6{}400\text{ N}

and a downward gravitational force (weight) of

W = mg = 500\text{ kg} \times 9.8\text{ m/s}^2 = 4{}900\text{ N}

. The net upward force is

6{}400\text{ N} - 4{}900\text{ N} = 1{}500\text{ N}

. Applying Newton's second law (

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

) gives an acceleration of

1{}500\text{ N} / 500\text{ kg} = 3\text{ m/s}^2

.

Step-by-Step Solution

1

Calculate the downward gravitational force (weight) acting on the container.

W = mg = 500\text{ kg} \times 9.8\text{ m/s}^2 = 4{}900\text{ N}

Weight is the force exerted on the mass by gravity.

2

Find the net upward force by subtracting weight from the upward cable tension.

F_{\text{net}} = F_{\text{tension}} - W = 6{}400\text{ N} - 4{}900\text{ N} = 1{}500\text{ N}

The acceleration depends on the resultant unbalanced force acting on the object.

3

Apply Newton's second law (

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

) to determine the acceleration.

a = \frac{1{}500\text{ N}}{500\text{ kg}} = 3\text{ m/s}^2

Acceleration equals net force divided by total mass.

Key Concept

Newton's Second Law and Net Vertical Force

Estimated Time:1m 0s

Question 20Question →

In the study of classical mechanics, various terms describe the motion of bodies and the forces acting upon them. Match each mechanics concept 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

Momentum corresponds to the product of mass and velocity; Acceleration corresponds to the rate of change of velocity; Inertia corresponds to the resistance to change in motion; Weight corresponds to the gravitational force acting on an object's mass.

Each mechanics term addresses a specific physical property or relationship: Momentum measures the quantity of motion (

p = mv

), Acceleration measures how fast velocity changes (

a = \frac{\Delta v}{\Delta t}

), Inertia is the inherent resistance to changes in motion, and Weight is the gravitational force acting on mass (

W = mg

).

Step-by-Step Solution

1

Identify the definition of Momentum

Momentum is mathematically defined as mass multiplied by velocity (

p = mv

), which matches the statement regarding the quantity of motion.

Momentum quantifies the kinetic impact and difficulty of stopping a moving object.

2

Identify the definition of Acceleration

Acceleration is the derivative or rate of change of velocity over time (

a = \frac{\Delta v}{\Delta t}

), matching the definition involving changes in speed or direction.

Any vector change in velocity over time constitutes acceleration.

3

Identify the definition of Inertia

Inertia corresponds to Newton's first law concept—the inherent tendency of matter to resist alterations to its motion or rest.

Inertia is a property of mass rather than a force or rate.

4

Identify the definition of Weight

Weight is the gravitational force exerted on a mass (

W = mg

), matching the downward planetary force definition.

Unlike invariant mass, weight is a force that changes based on local gravity.

Key Concept

Distinguishing core classical mechanics concepts: momentum, acceleration, inertia, and weight.

Estimated Time:1m 0s

Mechanics and Motion

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