Mechanics and Motion Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) — Page 2

Question 21Question →

A warehouse forklift applies a constant horizontal forward force of $300\text{ N}$ to a $120\text{ kg}$ cargo pallet moving across a level floor. A constant opposing friction force of $60\text{ N}$ acts against the pallet. What is the magnitude of the pallet's acceleration in $\text{m/s}^2$ ?

Show answer & explanation

Answer: 2

Answer

The magnitude of the pallet's acceleration is

2\text{ m/s}^2

.

According to Newton's second law of motion, the acceleration of an object equals the net unbalanced force acting upon it divided by its mass (

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

). The net force is the forward applied force minus opposing friction (

300\text{ N} - 60\text{ N} = 240\text{ N}

). Dividing

240\text{ N}

by the mass of

120\text{ kg}

yields an acceleration of

2\text{ m/s}^2

.

Step-by-Step Solution

1

Determine the net horizontal force acting on the object by combining all horizontal force components.

F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}} = 300\text{ N} - 60\text{ N} = 240\text{ N}

Forces in opposite directions subtract to yield the overall resultant force causing acceleration.

2

Use Newton's second law (

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

) to solve for acceleration (

a

).

a = \frac{F_{\text{net}}}{m} = \frac{240\text{ N}}{120\text{ kg}} = 2\text{ m/s}^2

Acceleration is directly proportional to net force and inversely proportional to mass.

Key Concept

Newton's Second Law of Motion (

F_{\text{net}} = ma

) with opposing frictional forces

Estimated Time:1m 0s

Question 22Question →

A robotic exploration rover has a mass of $120\text{ kg}$ on Earth. The rover is transported to Mars, where the acceleration due to gravity is approximately $3.7\text{ m/s}^2$ . If the rover accelerates horizontally across a flat, level surface at $2.0\text{ m/s}^2$ , what is the magnitude of the horizontal net force acting on the rover?

24\text{ N}

240\text{ N}

444\text{ N}

684\text{ N}

Show answer & explanation

Answer: $240\text{ N}$

Answer

The magnitude of the horizontal net force acting on the rover is

240\text{ N}

.

According to Newton's Second Law of Motion (

F = ma

), the net force acting on an object is equal to its mass multiplied by its acceleration. An object's mass is invariant across different gravitational fields. Therefore, accelerating a

120\text{ kg}

rover horizontally at

2.0\text{ m/s}^2

requires a horizontal net force of

120\text{ kg} \times 2.0\text{ m/s}^2 = 240\text{ N}

.

Step-by-Step Solution

1

Identify the relevant physical law and given values.

Mass

m = 120\text{ kg}

, horizontal acceleration

a = 2.0\text{ m/s}^2

, and Newton's Second Law

F_{\text{net}} = ma

.

Mass is an intrinsic scalar property that remains constant regardless of location or local gravity.

2

Calculate the horizontal net force required to accelerate the mass.

F_{\text{net}} = 120\text{ kg} \times 2.0\text{ m/s}^2 = 240\text{ N}

.

Horizontal acceleration is governed strictly by the horizontal net force and mass, independent of vertical gravitational forces on a level surface.

Key Concept

Newton's Second Law of Motion and Independence of Mass from Gravity

Estimated Time:1m 0s

Question 23Question →

In the study of classical mechanics and physical motion, different principles govern how forces influence bodies at rest and in motion. Match each mechanics concept on the left with its correct physical description on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Static friction matches the resistive force opposing the start of sliding motion; terminal velocity matches the constant speed reached when fluid resistance equals gravity; centripetal acceleration matches the inward rate of change of velocity along a curved trajectory; impulse matches the product of applied net force and time interval.

Each physical mechanics concept accurately pairs with its standard operational definition: static friction prevents the onset of relative sliding; terminal velocity occurs at fluid dynamic equilibrium when drag balances weight; centripetal acceleration governs directional change toward a circle's center; and impulse represents force applied over time to change momentum.

Step-by-Step Solution

1

Identify the definition of static friction

Matched to the resistive force opposing the start of sliding motion between stationary surfaces.

Static friction acts exclusively on objects at rest up to the threshold of motion.

2

Identify the definition of terminal velocity

Matched to the constant speed reached when upward fluid resistance equals downward gravity.

When drag balances weight, net force becomes zero, producing constant velocity during free fall.

3

Identify the definition of centripetal acceleration

Matched to the rate of change of velocity directed inward toward the center of a curved trajectory.

Inward acceleration is required to continuously alter the direction of velocity in curved motion.

4

Identify the definition of impulse

Matched to the product of an applied net force and the time interval.

Impulse is quantified as force multiplied by time duration (

J = F \Delta t

).

Key Concept

Fundamental concepts in classical mechanics: friction, equilibrium terminal motion, kinematics of circular paths, and momentum changes

Estimated Time:1m 0s

Question 24Question →

An electric delivery van with a total mass of $2,000\text{ kg}$ travels along a straight road at a constant velocity of $15\text{ m/s}$ . The driver applies the brakes, producing a constant opposing friction force of $6,000\text{ N}$ until the vehicle comes to a complete stop. How much time does it take for the van to stop?

20\text{ seconds}

5\text{ seconds}

50\text{ seconds}

45\text{ seconds}

Show answer & explanation

Answer: $5\text{ seconds}$

Answer

The total time required for the delivery van to come to a complete stop is

5\text{ seconds}

.

According to Newton's second law (

F = ma

), the opposing braking force of

6,000\text{ N}

acting on a

2,000\text{ kg}

vehicle produces an acceleration of

a = \frac{6,000\text{ N}}{2,000\text{ kg}} = 3\text{ m/s}^2

. To bring the vehicle from

15\text{ m/s}

to rest at a rate of

3\text{ m/s}^2

, the time needed is

t = \frac{\Delta v}{a} = \frac{15\text{ m/s}}{3\text{ m/s}^2} = 5\text{ seconds}

.

Step-by-Step Solution

1

Calculate the magnitude of deceleration using Newton's second law of motion (

F = ma

).

a = \frac{F}{m} = \frac{6,000\text{ N}}{2,000\text{ kg}} = 3\text{ m/s}^2

The net opposing force applied to the known mass determines the rate at which the vehicle slows down.

2

Determine the time required to reduce the velocity from

15\text{ m/s}

to

0\text{ m/s}

using the kinematic definition of acceleration (

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

).

t = \frac{15\text{ m/s}}{3\text{ m/s}^2} = 5\text{ seconds}

Uniform deceleration reduces speed at a constant rate of

3\text{ m/s}

each second until rest is reached.

Key Concept

Newton's Second Law of Motion and Linear Deceleration

Estimated Time:1m 0s

Question 25Question →

A conveyor system accelerates a $15\text{ kg}$ package along a straight horizontal track from an initial speed of $2\text{ m/s}$ to a final speed of $8\text{ m/s}$ in $3\text{ seconds}$ . What is the magnitude of the net horizontal force acting on the package, in newtons?

Show answer & explanation

Answer: 30

Answer

The magnitude of the net horizontal force acting on the package is

30\text{ N}

.

By finding the acceleration through

a = \frac{v_f - v_i}{t} = \frac{8 - 2}{3} = 2\text{ m/s}^2

and applying Newton's second law (

F = ma

), the resulting net force is

15\text{ kg} \times 2\text{ m/s}^2 = 30\text{ N}

.

Step-by-Step Solution

1

Determine the horizontal acceleration of the package using 1D kinematics.

a = \frac{8\text{ m/s} - 2\text{ m/s}}{3\text{ s}} = \frac{6\text{ m/s}}{3\text{ s}} = 2\text{ m/s}^2

Acceleration measures the rate of change of velocity over elapsed time (

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

).

2

Calculate the net force by applying Newton's second law of motion.

F_{\text{net}} = m \times a = 15\text{ kg} \times 2\text{ m/s}^2 = 30\text{ N}

Net force is directly proportional to the mass and the acceleration of the object (

F = ma

).

Key Concept

Newton's Second Law and Uniform Acceleration

Estimated Time:1m 0s

Question 26Question →

A $400\text{ kg}$ patrol boat accelerates uniformly from rest to a speed of $18\text{ m/s}$ in $6\text{ seconds}$ across calm water. If a constant hydrodynamic resistance force of $300\text{ N}$ opposes the motion, what forward thrust force must the boat's engine produce?

1,200\text{ N}

1,500\text{ N}

900\text{ N}

4,200\text{ N}

Show answer & explanation

Answer: $1,500\text{ N}$

Answer

The boat's engine must produce a forward thrust of

1,500\text{ N}

.

To find the total thrust, first determine the acceleration from the velocity change (

18\text{ m/s} \div 6\text{ s} = 3\text{ m/s}^2

). Using Newton's Second Law (

F = ma

), the net forward force required is

400\text{ kg} \times 3\text{ m/s}^2 = 1,200\text{ N}

. Because

300\text{ N}

of water resistance opposes the boat, the engine must supply enough forward force to overcome drag plus provide the net accelerating force:

1,200\text{ N} + 300\text{ N} = 1,500\text{ N}

.

Step-by-Step Solution

1

Calculate the acceleration of the patrol boat using kinematic relations.

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

Uniform acceleration is defined as the change in velocity divided by the elapsed time.

2

Determine the net horizontal force required to accelerate the boat using Newton's Second Law.

F_{\text{net}} = m \cdot a = 400\text{ kg} \times 3\text{ m/s}^2 = 1,200\text{ N}

The net force acting on any mass is directly proportional to its acceleration (

F = ma

).

3

Apply the net force equation along the horizontal axis to solve for engine thrust.

F_{\text{thrust}} - F_{\text{resistance}} = F_{\text{net}} \implies F_{\text{thrust}} = 1,200\text{ N} + 300\text{ N} = 1,500\text{ N}

The engine thrust must overcome the backward resistive drag while providing the remaining force needed for forward acceleration.

Key Concept

Newton's Second Law and Net Force in One Dimension

Estimated Time:1m 0s

Question 27Question →

In the study of classical mechanics, different physical quantities and forces describe how objects move and interact. Match each mechanical concept with its correct physical definition.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Displacement matches with the straight-line vector from starting to final position; Average speed matches with total path distance divided by elapsed time; Normal force matches with the perpendicular support force exerted by a surface; Unbalanced force matches with a non-zero net force causing a change in velocity.

Each concept correctly aligns with its precise definition in classical kinematics and dynamics: displacement measures the net position vector, average speed measures scalar distance over time, the normal force provides perpendicular support, and an unbalanced force produces net acceleration.

Step-by-Step Solution

1

Identify the spatial vector measurement between two points.

Displacement represents the straight-line path and direction from initial to final position.

Unlike total distance, displacement depends only on the starting and ending positions.

2

Identify the scalar measure of motion rate.

Average speed equals total path distance divided by time elapsed.

Speed is scalar and does not take direction into account.

3

Identify the perpendicular contact force.

Normal force is the perpendicular push provided by a surface supporting a mass.

In physics, 'normal' means perpendicular to the contact plane.

4

Identify the cause of mechanical acceleration.

An unbalanced force produces a non-zero net force that accelerates an object.

Balanced forces maintain constant velocity (equilibrium), whereas unbalanced forces change motion.

Key Concept

Kinematic vector and scalar quantities alongside contact and net forces in mechanics

Estimated Time:1m 0s

Question 28Question →

A motorized winch pulls a $250\text{ kg}$ equipment sled across a level, frictionless sheet of ice. If the winch exerts a constant horizontal force of $750\text{ N}$ starting from rest, what is the speed of the sled, in meters per second ( $\text{m/s}$ ), after $4\text{ seconds}$ ?

Show answer & explanation

Answer: 12

Answer

The sled reaches a speed of

12\text{ m/s}

after

4\text{ seconds}

.

Applying Newton's second law gives an acceleration of

a = \frac{F}{m} = \frac{750\text{ N}}{250\text{ kg}} = 3\text{ m/s}^2

. Since the sled begins at rest (

v_0 = 0

), its speed after

4\text{ s}

is

v = at = 3\text{ m/s}^2 \times 4\text{ s} = 12\text{ m/s}

.

Step-by-Step Solution

1

Determine the acceleration produced by the net horizontal force

a = \frac{F_{\text{net}}}{m} = \frac{750\text{ N}}{250\text{ kg}} = 3\text{ m/s}^2

According to Newton's second law of motion (

F = ma

), acceleration equals the net force divided by mass.

2

Calculate final speed from initial rest and constant acceleration over time

v = v_0 + at = 0\text{ m/s} + (3\text{ m/s}^2)(4\text{ s}) = 12\text{ m/s}

Uniform acceleration kinematic equation relates velocity change to acceleration multiplied by elapsed time.

Key Concept

Combining Newton's second law (

F = ma

) with linear kinematics (

v = v_0 + at

) to determine final velocity under constant net force.

Alternative Method

Use the impulse-momentum theorem:

\text{Impulse} = F \cdot \Delta t = \Delta p = m \cdot v

. Substituting known values gives

(750\text{ N})(4\text{ s}) = (250\text{ kg})(v) \implies 3,000\text{ N}\cdot\text{s} = 250\text{ kg} \cdot v \implies v = \frac{3,000}{250} = 12\text{ m/s}

.

Estimated Time:1m 0s

Question 29Question →

An equipment container weighs $120\text{ N}$ on Earth, where the acceleration due to gravity is approximately $10\text{ m/s}^2$ . The container is transported to an orbital space station where it is in a weightless environment. If an astronaut applies a constant net horizontal force of $36\text{ N}$ to the container, what is its resulting acceleration?

0.3\text{ m/s}^2

30\text{ m/s}^2

3\text{ m/s}^2

3\text{ m/s}

Show answer & explanation

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

Answer

3\text{ m/s}^2

Mass measures an object's inertia and does not change when moving between Earth and orbit. Using the Earth weight

W = 120\text{ N}

and gravity

g = 10\text{ m/s}^2

, the container's mass is

m = 12\text{ kg}

. In orbit, applying a net force of

36\text{ N}

yields an acceleration of

a = F/m = 36\text{ N} / 12\text{ kg} = 3\text{ m/s}^2

.

Step-by-Step Solution

1

Determine the mass of the container from its Earth weight

\text{Mass } m = \frac{W}{g} = \frac{120\text{ N}}{10\text{ m/s}^2} = 12\text{ kg}

Weight is the force of gravity acting on mass (

W = mg

). Mass is an intrinsic property of the object and remains unchanged regardless of location.

2

Apply Newton's Second Law of Motion (

F = ma

) in the orbital environment

a = \frac{F_{\text{net}}}{m} = \frac{36\text{ N}}{12\text{ kg}} = 3\text{ m/s}^2

Although the container is weightless in orbit, its inertia (mass) remains

12\text{ kg}

. A net force produces an acceleration inversely proportional to that mass.

Key Concept

Newton's Second Law (

F = ma

) and the distinction between mass (inertia) and weight (gravitational force).

Estimated Time:1m 0s

Question 30Question →

A light training aircraft with a mass of $750\text{ kg}$ accelerates from rest along a straight runway under a constant net forward force of $1{}500\text{ N}$ . What is the velocity of the aircraft, in meters per second ( $\text{m/s}$ ), after $8\text{ seconds}$ ?

Show answer & explanation

Answer: 16

Answer

16 m/s

According to Newton's second law (

F = ma

), a net force of

1{}500\text{ N}

applied to a mass of

750\text{ kg}

produces a constant acceleration of

a = \frac{1{}500}{750} = 2\text{ m/s}^2

. Starting from rest (

v_0 = 0

), the velocity after

8\text{ seconds}

is

v = at = 2\text{ m/s}^2 \times 8\text{ s} = 16\text{ m/s}

.

Step-by-Step Solution

1

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

F_{\text{net}} = ma

).

a = \frac{1{}500\text{ N}}{750\text{ kg}} = 2\text{ m/s}^2

Acceleration is directly proportional to net force and inversely proportional to mass.

2

Calculate the final velocity after

8\text{ seconds}

using the kinematic equation for uniform acceleration (

v = v_0 + at

).

v = 0\text{ m/s} + (2\text{ m/s}^2)(8\text{ s}) = 16\text{ m/s}

Starting from rest, the final velocity equals the constant acceleration multiplied by elapsed time.

Key Concept

Newton's Second Law and Uniform Acceleration

Alternative Method

Apply the impulse-momentum theorem:

\text{Impulse} = F_{\text{net}} \times \Delta t = \Delta p = m \times v

. Solving for velocity gives

v = \frac{F_{\text{net}} \times \Delta t}{m} = \frac{1{}500\text{ N} \times 8\text{ s}}{750\text{ kg}} = \frac{12{}000}{750} = 16\text{ m/s}

.

Estimated Time:1m 0s

Question 31Question →

A rescue drone with a mass of $40\text{ kg}$ is ascending vertically. If the drone's motors generate a constant upward lift force of $520\text{ N}$ in an area where the acceleration due to gravity is $8\text{ m/s}^2$ , what is the net upward acceleration of the drone?

13\text{ m/s}^2

21\text{ m/s}^2

5\text{ m/s}^2

0.5\text{ m/s}^2

Show answer & explanation

Answer: $5\text{ m/s}^2$

Answer

5\text{ m/s}^2

The upward thrust of

520\text{ N}

is opposed by the downward gravitational force of

320\text{ N}

(

40\text{ kg} \times 8\text{ m/s}^2

). The resulting net upward force is

200\text{ N}

. Dividing this net force by the mass of

40\text{ kg}

gives an upward acceleration of

5\text{ m/s}^2

.

Step-by-Step Solution

1

Calculate the downward force of gravity (weight) acting on the drone.

W = m \times g = 40\text{ kg} \times 8\text{ m/s}^2 = 320\text{ N}

downward.

Gravity exerts a constant downward force equal to the product of mass and local gravitational acceleration.

2

Determine the net vertical force acting on the drone.

F_{\text{net}} = F_{\text{lift}} - W = 520\text{ N} - 320\text{ N} = 200\text{ N}

upward.

The upward lift and downward weight act in opposite directions along the vertical axis, so their magnitudes subtract.

3

Apply Newton's second law (

F_{\text{net}} = ma

) to solve for acceleration.

a = \frac{F_{\text{net}}}{m} = \frac{200\text{ N}}{40\text{ kg}} = 5\text{ m/s}^2

.

Acceleration equals the net unbalanced force divided by the total mass of the object.

Key Concept

Newton's Second Law and Net Force in Vertical Motion

Alternative Method

Calculate the upward acceleration produced by the motor thrust alone (

a_{\text{thrust}} = \frac{520\text{ N}}{40\text{ kg}} = 13\text{ m/s}^2

) and subtract the downward acceleration due to gravity (

8\text{ m/s}^2

), which gives

13\text{ m/s}^2 - 8\text{ m/s}^2 = 5\text{ m/s}^2

.

Estimated Time:1m 0s

Question 32Question →

A robotic transport carrier with a mass of $200\text{ kg}$ starts from rest and accelerates uniformly along a straight track, reaching a final velocity of $15\text{ m/s}$ in $5\text{ s}$ . What is the magnitude of the net force acting on the carrier?

60\text{ N}

600\text{ N}

6{}000\text{ N}

300\text{ N}

Show answer & explanation

Answer: $600\text{ N}$

Answer

600\text{ N}

The correct answer is

600\text{ N}

. First, find the constant acceleration by dividing the change in velocity by elapsed time:

a = \frac{15\text{ m/s}}{5\text{ s}} = 3\text{ m/s}^2

. Next, use Newton's second law of motion (

F = ma

) to find the net force:

F = 200\text{ kg} \times 3\text{ m/s}^2 = 600\text{ N}

.

Step-by-Step Solution

1

Calculate the linear acceleration using the kinematic formula

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

.

a = \frac{15\text{ m/s} - 0\text{ m/s}}{5\text{ s}} = 3\text{ m/s}^2

Acceleration represents the rate at which velocity changes over time.

2

Apply Newton's second law of motion (

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

).

F_{\text{net}} = 200\text{ kg} \times 3\text{ m/s}^2 = 600\text{ N}

The net force required to accelerate an object is equal to the product of its mass and its acceleration.

Key Concept

Newton's Second Law of Motion and Kinematic Acceleration

Estimated Time:45s

Question 33Question →

In classical mechanics, specific physical quantities and principles describe how bodies move and respond to applied forces. Match each mechanical 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

Inertia matches the natural tendency of an object to resist any change in its state of rest or motion; Acceleration matches the rate at which an object changes its velocity with respect to time; Linear Momentum matches the product of an object's mass and its velocity; Centripetal Force matches a net inward force directed toward the center of curvature that maintains circular motion.

Inertia is the tendency of matter to resist changes in motion; acceleration is the time derivative/rate of change of velocity; linear momentum represents mass in motion (

p = mv

); and centripetal force is the inward radial force that continuously changes the direction of an object in circular motion.

Step-by-Step Solution

1

Identify the definition of Inertia

Inertia corresponds to the property of mass resisting alterations in its state of rest or uniform motion.

According to Newton's First Law of Motion, inertia is an intrinsic resistance to acceleration.

2

Identify the definition of Acceleration

Acceleration corresponds to the rate of change of velocity over time (

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

).

Acceleration describes how rapidly speed or direction changes over a given time interval.

3

Identify the definition of Linear Momentum

Linear Momentum corresponds to mass multiplied by velocity (

p = mv

).

Momentum quantifies the motion of a mass and is conserved in isolated systems.

4

Identify the definition of Centripetal Force

Centripetal Force corresponds to the center-seeking net force in circular motion (

F_c = \frac{mv^2}{r}

).

An inward radial force is required to continuously deflect an object's velocity vector along a curve.

Key Concept

Fundamental definitions and kinematic relationships governing linear and circular mechanics.

Estimated Time:1m 0s

Question 34Question →

A lunar rover has a mass of $90\text{ kg}$ on Earth. While operating on the lunar surface, where gravitational acceleration is approximately $1.6\text{ m/s}^2$ , its electric drive system generates a constant net forward force of $270\text{ N}$ . What is the forward acceleration of the rover?

18.0\text{ m/s}^2

3.0\text{ m/s}^2

4.6\text{ m/s}^2

0.3\text{ m/s}^2

Show answer & explanation

Answer: $3.0\text{ m/s}^2$

Answer

The forward acceleration of the rover is

3.0\text{ m/s}^2

.

According to Newton's second law of motion, acceleration is directly proportional to the net force applied and inversely proportional to the mass (

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

). Because mass is constant regardless of location, the rover's mass on the Moon is still

90\text{ kg}

. Dividing the net force of

270\text{ N}

by

90\text{ kg}

yields an acceleration of

3.0\text{ m/s}^2

.

Step-by-Step Solution

1

Identify the invariant mass of the rover

m = 90\text{ kg}

Mass measures the amount of matter in an object and remains constant regardless of local gravity.

2

Apply Newton's second law of motion (

F_{\text{net}} = ma

)

a = \frac{F_{\text{net}}}{m} = \frac{270\text{ N}}{90\text{ kg}} = 3.0\text{ m/s}^2

Horizontal acceleration depends solely on the net horizontal force divided by the object's mass.

Key Concept

Newton's Second Law of Motion and Mass Invariance

Estimated Time:1m 0s

Question 35Question →

In physical science and mechanics, fundamental physical principles govern how forces determine the motion of bodies and systems. Match each physical law to its precise operational description.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Newton's First Law matches constant velocity under zero net external force; Newton's Second Law matches acceleration directly proportional to net force and inversely proportional to mass; Newton's Third Law matches simultaneous equal and opposite forces exerted between two interacting bodies; the Law of Conservation of Linear Momentum matches constant total vector momentum in an isolated system.

Each law corresponds to its specific physical definition: Newton's First Law governs the inertia of objects when net force is zero; Newton's Second Law relates net force to mass and acceleration; Newton's Third Law defines equal and opposite interaction pairs acting on two distinct bodies; and the Law of Conservation of Linear Momentum dictates that total momentum remains constant in an isolated system without external forces.

Step-by-Step Solution

1

Analyze the conditions for inertia and equilibrium governed by Newton's First Law.

Identify that a body in motion at constant velocity or at rest requires zero net external force to maintain that state.

Inertia represents the natural resistance of any physical body to a change in its state of velocity.

2

Determine the quantitative formulation linking net force, mass, and acceleration for Newton's Second Law.

Match the law to the relation

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

, representing acceleration produced by an unbalanced force.

Newton's Second Law provides the fundamental equation of dynamics relating force inputs to kinematic acceleration.

3

Examine the nature of action-reaction force pairs acting across interacting objects for Newton's Third Law.

Match the law to simultaneous, equal-magnitude, opposite-direction forces acting on separate bodies.

Action-reaction pairs act on different objects and therefore cannot cancel each other out to prevent individual body acceleration.

4

Evaluate the state of total vector momentum in a closed physical system for Conservation of Linear Momentum.

Match the law to the constancy of total vector momentum when external net forces are absent.

In the absence of external net forces, the time derivative of total system momentum is zero.

Key Concept

Fundamental Newtonian mechanics principles and conservation laws governing forces, acceleration, inertia, and momentum.

Question 36Question →

A maintenance cart with a mass of $250\text{ kg}$ travels along a straight horizontal track. If the cart uniformly slows down from an initial velocity of $15\text{ m/s}$ due east to $5\text{ m/s}$ due east over a time interval of $5\text{ seconds}$ , what is the magnitude and direction of the net force acting on the cart?

500\text{ N}

directed due east

500\text{ N}

directed due west

4{}900\text{ N}

directed due west

0.5\text{ N}

directed due west

Show answer & explanation

Answer: $500\text{ N}$ directed due west

Answer

The magnitude of the net force is

500\text{ N}

, directed due west.

Acceleration is the change in velocity divided by time:

a = (5\text{ m/s} - 15\text{ m/s}) / 5\text{ s} = -2\text{ m/s}^2

. The negative sign indicates an acceleration directed due west (opposite to the eastward motion). Applying Newton's Second Law (

F = ma

), the net force is

250\text{ kg} \times 2\text{ m/s}^2 = 500\text{ N}

directed due west.

Step-by-Step Solution

1

Calculate the acceleration using the kinematics formula

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

.

a = \frac{5\text{ m/s} - 15\text{ m/s}}{5\text{ s}} = \frac{-10\text{ m/s}}{5\text{ s}} = -2\text{ m/s}^2

(or

2\text{ m/s}^2

directed west).

Acceleration is the rate of change of velocity over time.

2

Calculate the magnitude and direction of the net force using Newton's Second Law,

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

.

F_{\text{net}} = 250\text{ kg} \times 2\text{ m/s}^2 = 500\text{ N}

directed west.

Net force is equal to mass multiplied by acceleration and always points in the same direction as the acceleration vector.

Key Concept

Newton's Second Law of Motion (

F_{\text{net}} = ma

) and Kinematics of Linear Deceleration

Alternative Method

Use the impulse-momentum theorem (

F_{\text{net}} \cdot \Delta t = m \cdot \Delta v

). Here,

\Delta p = 250\text{ kg} \times (5\text{ m/s} - 15\text{ m/s}) = -2{}500\text{ kg}\cdot\text{m/s}

. Dividing momentum change by

\Delta t = 5\text{ s}

yields

F_{\text{net}} = -500\text{ N}

, meaning

500\text{ N}

directed west.

Estimated Time:1m 0s

Question 37Question →

In classical mechanics, fundamental laws and principles define how forces govern the motion and interaction of physical bodies. Match each mechanical principle with its correct scientific definition or governing rule.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Newton's First Law pairs with the statement describing an object maintaining constant velocity unless acted upon by a net force; Newton's Second Law pairs with the statement that acceleration is directly proportional to net force and inversely proportional to mass; Newton's Third Law pairs with the statement regarding equal and opposite force interactions between two bodies; and the Law of Conservation of Momentum pairs with the statement that total mass times velocity remains constant in a closed system.

Each mechanical principle aligns directly with its formal physical definition: Newton's First Law governs inertia and zero-acceleration states; Newton's Second Law defines how net force produces acceleration proportional to force and inversely proportional to mass; Newton's Third Law defines equal and opposite force pairs between interacting bodies; and the Law of Conservation of Momentum dictates the invariance of total system momentum in closed systems.

Step-by-Step Solution

1

Identify the foundational definition of inertia and unaccelerated motion.

Newton's First Law matches the description of objects maintaining rest or uniform straight-line motion unless a net external force intervenes.

Inertia requires zero net force for constant velocity.

2

Identify the quantitative relationship governing net force, acceleration, and mass.

Newton's Second Law matches the relationship where acceleration is proportional to net force and inversely proportional to mass (

F_{\text{net}} = ma

).

This law provides the direct causal formula for changing an object's velocity.

3

Identify the law governing reciprocal force pairs between interacting objects.

Newton's Third Law matches the statement of equal and opposite forces acting simultaneously on two separate bodies.

Forces in nature always exist in matched action-reaction pairs across interacting bodies.

4

Identify the principle governing total quantity of motion across collisions in isolated systems.

The Law of Conservation of Momentum matches the constant total vector product of mass and velocity (

mv

) in closed systems.

Internal interaction forces cancel out vectorially across the entire system, preserving total momentum.

Key Concept

Fundamental Principles and Governing Laws of Classical Mechanics

Estimated Time:1m 0s

Mechanics and Motion

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