AP Physics C: Mechanics 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 14 questions to check your progress.

Question 1 of 14

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

A)The object's change in kinetic energy.B)The integral of the net force exerted on the object over a time interval.C)The rate of change of the object's momentum.D)The product of the object's mass and its final velocity.

All Questions (14)

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

A) The object's change in kinetic energy.

B) The integral of the net force exerted on the object over a time interval.

C) The rate of change of the object's momentum.

D) The product of the object's mass and its final velocity.

Correct Answer: B

According to the provided content, impulse is defined as the integral of a force exerted on an object or system over a time interval. The relevant equation is J = ∫F_net(t)dt.

The impulse-momentum theorem establishes a direct relationship between which two quantities?

A) Net force and change in momentum.

B) Impulse and change in momentum.

C) Net force and impulse.

D) Impulse and final momentum.

Correct Answer: B

The provided content states that the impulse-momentum theorem relates the impulse delivered to an object and the object's change in momentum, as shown by the equation J = Δp.

The equation F_net = dp/dt expresses that the net external force on a system is equal to:

A) the impulse delivered to the system.

B) the change in the system's momentum.

C) the rate of change of the system's momentum.

D) the integral of the system's momentum over time.

Correct Answer: C

Content point 3 explicitly states that the rate of change of a system's momentum is equal to the net external force exerted on that system, corresponding to the equation F_net = dp/dt.

An object's momentum changes from an initial value p_i to a final value p_f. According to the impulse-momentum theorem, what is the impulse J delivered to the object?

A) J = p_f

B) J = p_i

C) J = p_f - p_i

D) J = p_f + p_i

Correct Answer: C

The impulse-momentum theorem is J = Δp. The change in any quantity (Δ) is the final value minus the initial value. Therefore, Δp = p_f - p_i, which means J = p_f - p_i.

A graph of the net force on an object versus time is created. The area under the curve between time t1 and time t2 represents which of the following?

A) The average net force on the object.

B) The final momentum of the object.

C) The acceleration of the object.

D) The change in momentum of the object.

Correct Answer: D

The definition of impulse is the integral of net force over time, J = ∫F_net(t)dt, which is the area under a Force vs. Time graph. The impulse-momentum theorem states that J = Δp. Therefore, the area under the curve is equal to the change in momentum.

If the net external force on a system is zero over a given time interval, what must be true about the system's momentum during that interval?

A) The momentum must be zero.

B) The momentum must be constant.

C) The momentum must be changing at a constant rate.

D) The momentum must be increasing.

Correct Answer: B

From the equation F_net = dp/dt, if F_net is zero, then dp/dt must be zero. This means that the momentum p is not changing with time; it is constant. Consequently, the change in momentum Δp is also zero.

Which equation represents the mathematical definition of impulse?

A) J = Δp

B) F_net = dp/dt

C) J = ∫F_net(t)dt

D) p = mv

Correct Answer: C

Content point 4 explicitly defines impulse as the integral of a force exerted on an object or system over a time interval, with the relevant equation J = ∫F_net(t)dt.

Two objects receive the same impulse. Object A experiences the impulse over 2 seconds, while Object B experiences it over 4 seconds. How does the average net force on Object A (F_A) compare to the average net force on Object B (F_B)?

A) F_A = 2 * F_B

B) F_A = 0.5 * F_B

C) F_A = F_B

D) F_A = 4 * F_B

Correct Answer: A

Impulse J is related to average force F_avg and time Δt by J = F_avg * Δt. Since the impulse (J) is the same for both objects, F_A * Δt_A = F_B * Δt_B. Plugging in the times, F_A * (2s) = F_B * (4s). Solving for F_A gives F_A = (4/2) * F_B, or F_A = 2 * F_B.

The relationship F_net = dp/dt can be rearranged and integrated over a time interval from t1 to t2. This mathematical process directly leads to which of the following principles?

A) The law of conservation of energy.

B) The definition of acceleration.

C) The impulse-momentum theorem.

D) Newton's Third Law.

Correct Answer: C

Rearranging gives dp = F_net * dt. Integrating both sides from the initial state to the final state gives ∫dp = ∫F_net * dt. This evaluates to Δp = J, which is the impulse-momentum theorem.

A graph shows an object's momentum as a function of time. The slope of the tangent line to this graph at a specific time t represents which physical quantity?

A) The impulse on the object at that time.

B) The net external force on the object at that time.

C) The change in momentum of the object.

D) The object's velocity at that time.

Correct Answer: B

The relationship F_net = dp/dt states that the net force is the time derivative (rate of change) of momentum. In a graph of momentum (p) versus time (t), the derivative dp/dt is represented by the slope of the tangent line. Therefore, the slope is the net external force.

For a constant net force F_net applied over a time interval Δt, the integral J = ∫F_net(t)dt simplifies to:

A) J = F_net / Δt

B) J = F_net * Δt

C) J = Δp / Δt

D) J = F_net

Correct Answer: B

When the net force is constant, it can be taken out of the integral. The integral of dt from t1 to t2 is simply the time interval Δt. Therefore, the equation simplifies to J = F_net * Δt.

Impulse (J) and momentum (p) are both vector quantities. Based on the impulse-momentum theorem (J = Δp), what is the relationship between the direction of the impulse and the direction of the change in momentum?

A) They are always in opposite directions.

B) They are always perpendicular to each other.

C) They are always in the same direction.

D) Their directions are unrelated.

Correct Answer: C

The equation J = Δp is a vector equation. For two vectors to be equal, both their magnitudes and their directions must be identical. Therefore, the direction of the impulse vector must be the same as the direction of the change in momentum vector.

To calculate the total change in momentum of an object subjected to a net force that varies with time, one must:

A) multiply the maximum force by the total time.

B) differentiate the force function with respect to time.

C) integrate the net force function over the relevant time interval.

D) find the average of the initial and final forces.

Correct Answer: C

The impulse-momentum theorem states J = Δp. The definition of impulse for a time-varying force is J = ∫F_net(t)dt. Therefore, to find the change in momentum (Δp), one must calculate the impulse by integrating the net force over the time interval.

Which statement provides the most fundamental connection between Newton's Second Law and the concept of impulse?

A) The impulse is the integral of the net force with respect to time, and the net force is the derivative of momentum with respect to time, making them inverse operations.

B) Both impulse and net force are vector quantities that cause a change in an object's velocity.

C) The impulse-momentum theorem (J=Δp) is only valid when the net force is constant, which is a special case of Newton's Second Law.

D) Net force is defined as the change in momentum, while impulse is defined as the change in force.

Correct Answer: A

The core connection is mathematical. F_net = dp/dt shows force as the time-derivative of momentum. J = ∫F_net(t)dt shows impulse as the time-integral of force. Integration and differentiation are inverse operations. Integrating F_net = dp/dt over time directly yields the impulse-momentum theorem, Δp = J, linking all the concepts.