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AP Physics 1: Algebra-Based Practice Quiz: Change in Momentum and Impulse

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 16 questions to check your progress.

Question 1 of 16

Which of the following best defines the impulse delivered to an object?

All Questions (16)

Which of the following best defines the impulse delivered to an object?

A) The product of the average force exerted on the object and the time interval during which the force is exerted.

B) The rate at which the object's momentum is changing.

C) The object's mass multiplied by its final velocity.

D) The change in the object's kinetic energy.

Correct Answer: A

Based on the provided content, impulse is defined as the product of the average force exerted on a system and the time interval during which that force is exerted: $\vec{J} = \vec{F}_{avg} \Delta t$.

According to the impulse-momentum theorem, the impulse exerted on a system is equal to which of the following quantities?

A) The net external force on the system.

B) The system's change in momentum.

C) The system's final momentum.

D) The rate of change of the system's momentum.

Correct Answer: B

The provided content explicitly states the impulse-momentum theorem relates the impulse exerted on a system and the system's change in momentum: $\vec{J} = \Delta \vec{p}$.

The rate of change of momentum of an object is equivalent to which of the following?

A) The impulse delivered to the object.

B) The net external force exerted on the object.

C) The object's change in velocity.

D) The product of the average force and the time interval.

Correct Answer: B

Content point 3 states that the rate of change of momentum is equal to the net external force exerted on an object or system: $\vec{F}_{net} = \frac{\Delta \vec{p}}{\Delta t}$.

Impulse is a vector quantity. What determines the direction of the impulse vector?

A) The direction of the object's mass.

B) The direction of the object's initial velocity.

C) The direction of the net force exerted on the system.

D) The direction opposite to the change in momentum.

Correct Answer: C

Content point 5 states that impulse is a vector quantity and has the same direction as the net force exerted on the system.

A constant net force acts on an object for a time interval $\Delta t$. If the time interval is doubled while the force remains constant, what is the effect on the impulse delivered to the object?

A) The impulse is halved.

B) The impulse remains the same.

C) The impulse is doubled.

D) The impulse is quadrupled.

Correct Answer: C

Impulse is given by the equation $\vec{J} = \vec{F}_{avg} \Delta t$. If the average force $\vec{F}_{avg}$ is constant and the time interval $\Delta t$ is doubled, the impulse $\vec{J}$ will also be doubled.

In many real-world collisions, such as a bat hitting a baseball, the contact time is very short. To minimize the average force experienced by an object for a given change in momentum, what must be done?

A) The time interval of the interaction must be increased.

B) The time interval of the interaction must be decreased.

C) The object's mass must be increased.

D) The object's final velocity must be zero.

Correct Answer: A

From the impulse-momentum theorem, $\vec{F}_{avg} = \frac{\Delta \vec{p}}{\Delta t}$. To decrease the average force ($\vec{F}_{avg}$) for a constant change in momentum ($\Delta \vec{p}$), the time interval ($\Delta t$) must be increased.

How is Newton's second law of motion, $\vec{F}=m\vec{a}$, related to the impulse-momentum theorem?

A) They are completely independent physical laws.

B) The impulse-momentum theorem is only valid for systems with changing mass.

C) Newton's second law is a direct result of the impulse-momentum theorem for systems with constant mass.

D) The impulse-momentum theorem is a more general form of Newton's first law.

Correct Answer: C

Content point 7 explicitly states that Newton's second law of motion is a direct result of the impulse-momentum theorem applied to systems with constant mass.

An object's momentum is changing at a constant, non-zero rate. What can be concluded about the net external force on the object?

A) The net external force is zero.

B) The net external force is constant and non-zero.

C) The net external force is changing.

D) The net external force is perpendicular to the change in momentum.

Correct Answer: B

The relationship $\vec{F}_{net} = \frac{\Delta \vec{p}}{\Delta t}$ means that the net force is equal to the rate of change of momentum. If this rate is constant and non-zero, the net force must also be constant and non-zero.

Two objects of equal mass are moving towards a wall at the same speed. Object 1 stops upon impact, while Object 2 bounces back with the same speed. Which statement correctly compares the impulse delivered by the wall to each object?

A) Object 1 experiences a greater impulse.

B) Object 2 experiences a greater impulse.

C) Both objects experience the same non-zero impulse.

D) Both objects experience zero impulse.

Correct Answer: B

Impulse equals the change in momentum ($\Delta \vec{p}$). Object 1's momentum changes from $mv$ to 0, a change of magnitude $mv$. Object 2's momentum changes from $mv$ to $-mv$, a change of magnitude $2mv$. Since Object 2 has a larger change in momentum, it experiences a greater impulse.

A constant net force $\vec{F}$ is applied to an object, resulting in an impulse $\vec{J}$ over a time interval $\Delta t$. If a force of $2\vec{F}$ is applied for a time interval of $2\Delta t$, what is the new impulse delivered to the object?

A) $\vec{J}$

B) $2\vec{J}$

C) $4\vec{J}$

D) $\frac{1}{2}\vec{J}$

Correct Answer: C

The original impulse is $\vec{J} = \vec{F} \Delta t$. The new impulse is $\vec{J}_{new} = (2\vec{F})(2\Delta t) = 4 (\vec{F} \Delta t) = 4\vec{J}$.

Which of the following pairs of quantities are vector quantities with the same direction?

A) Impulse and mass

B) Net force and impulse

C) Time interval and momentum

D) Average force and speed

Correct Answer: B

Content point 5 states that impulse is a vector quantity and has the same direction as the net force exerted on the system. This is also evident from the equation $\vec{J} = \vec{F}_{avg} \Delta t$, where the scalar $\Delta t$ does not change the direction of the force vector.

An object at rest is subjected to a net force, causing its momentum to change by an amount $\Delta p$ in a time $\Delta t$. To achieve the same change in momentum $\Delta p$ in one-third of the time ($\Delta t/3$), what must be the magnitude of the new average force?

A) One-third of the original force.

B) The same as the original force.

C) Three times the original force.

D) Nine times the original force.

Correct Answer: C

From the relationship $\vec{F}_{avg} \Delta t = \Delta \vec{p}$, force and time are inversely proportional for a constant change in momentum. If the time is reduced to one-third, the average force must be multiplied by three to produce the same impulse and thus the same change in momentum.

The impulse-momentum theorem ($\vec{J} = \Delta \vec{p}$) is a restatement of which fundamental law?

A) Newton's First Law

B) Newton's Second Law

C) Newton's Third Law

D) The Law of Conservation of Energy

Correct Answer: B

The theorem is derived from Newton's Second Law. Rearranging $\vec{F}_{net} = \frac{\Delta \vec{p}}{\Delta t}$ gives $\vec{F}_{net}\Delta t = \Delta \vec{p}$. Since impulse $\vec{J} = \vec{F}_{net}\Delta t$, it follows that $\vec{J} = \Delta \vec{p}$. The content also states that Newton's second law is a direct result of the theorem, indicating they are fundamentally the same principle.

A ball is dropped and hits the floor. The net force on the ball is non-zero only during the brief time it is in contact with the floor. The impulse delivered by the floor to the ball is equal to:

A) The ball's momentum just before it hits the floor.

B) The ball's momentum just after it leaves the floor.

C) The vector difference between the ball's momentum after and before the collision.

D) The sum of the ball's momentum before and after the collision.

Correct Answer: C

The impulse-momentum theorem states that impulse is equal to the change in momentum, $\vec{J} = \Delta \vec{p}$. The change in momentum is defined as the final momentum minus the initial momentum ($\vec{p}_{final} - \vec{p}_{initial}$), which is the vector difference.

An object of mass $m$, initially at rest, is acted upon by a force $\vec{F}$ for a time $\Delta t$, resulting in an impulse $\vec{J}$. A second object of mass $2m$, also initially at rest, is acted upon by the same force $\vec{F}$ for the same time $\Delta t$. What is the impulse delivered to the second object?

A) $\frac{1}{2}\vec{J}$

B) $\vec{J}$

C) $2\vec{J}$

D) $4\vec{J}$

Correct Answer: B

Impulse is defined as $\vec{J} = \vec{F}_{avg} \Delta t$. The definition of impulse depends only on the average force and the time interval, not on the mass of the object. Since both the force and the time interval are the same for both objects, the impulse delivered is also the same.

The area under the curve on a net Force versus Time graph represents which of the following physical quantities?

A) Change in acceleration

B) Work done on the system

C) Change in momentum

D) Final velocity

Correct Answer: C

Impulse is defined as $\vec{J} = \vec{F}_{avg} \Delta t$. For a variable force, this corresponds to the integral of force with respect to time, which is the area under a Force-Time graph. According to the impulse-momentum theorem, impulse is equal to the change in momentum ($\vec{J} = \Delta \vec{p}$). Therefore, the area under the curve also represents the change in momentum.