AP Physics 1: Algebra-Based, AP exams, 10–15%

Unit 4: Linear Momentum

Unit 4 introduces momentum and impulse as the time-integrated view of force, then applies conservation of momentum to collisions and explosions. The distinction between elastic and inelastic collisions, and which quantity is conserved in each, is the central testable idea. Impulse from a force-versus-time graph is a frequent representation task.

Position: 4 of 8 units
Published weighting: 10–15% in the official framework
Topics covered: 4 topics in this guide

What is covered

Topics inside this unit.

These topics describe the scope students most often review for this part of AP Physics 1: Algebra-Based. Treat them as a study checklist rather than an exhaustive list of what a single exam form can sample.

Linear momentum: Momentum as mass times velocity, its vector nature, and its relationship to kinetic energy.
Change in momentum and impulse: Impulse as force applied over time, and the area under a force-versus-time graph.
Conservation of linear momentum: The conditions under which total momentum is conserved, and how system choice affects the analysis.
Elastic and inelastic collisions: What is conserved in each case, perfectly inelastic collisions, and explosions run in reverse.

Study tips

How to practice Linear Momentum.

Section-specific guidance that follows from how this material is usually tested.

Write momentum equations component by component; treating momentum as a scalar is the most common error.
Practice stating which quantities are conserved before computing anything in a collision problem.
Connect impulse to the safety-engineering examples the exam favors, such as crumple zones and padding.

Where this fits

Unit 4: Linear Momentum is 4 of 8 units in the AP Physics 1: Algebra-Based guide, and it carries a published weighting of 10–15% in the official framework. Use the full guide to balance it against everything else you have to review.

Back to the AP Physics 1: Algebra-Based guide Official exam information

Sample Linear Momentum questions

Practice questions, not yet expert-reviewed

Original practice questions written to the published framework for this section. No expert has reviewed them, and they are not taken from any official exam. Try each one before you open the answer.

Question 1Foundational
A 0.15 kg baseball travels at 40 m/s toward a catcher, who brings it completely to rest. What is the magnitude of the impulse the catcher's glove delivers to the ball?
1. A0.60 kg m/s
2. B3.0 kg m/s
3. C6.0 kg m/s
4. D60 kg m/s
Show answer
Answer: C. 6.0 kg m/s
Impulse equals the change in momentum: (0.15 kg)(40 m/s) = 6.0 kg m/s, directed opposite the ball's motion. The 0.60 kg m/s and 60 kg m/s choices both come from misplacing the decimal point in the mass.
Key insight: Impulse and momentum share the same units, so stopping an object always requires an impulse equal to its momentum.
Question 2Foundational
A 2.0 kg cart moving at 3.0 m/s on a frictionless track collides with a stationary 4.0 kg cart, and the two carts stick together. What is their common speed immediately after the collision?
1. A0.50 m/s
2. B1.0 m/s
3. C1.5 m/s
4. D3.0 m/s
Show answer
Answer: B. 1.0 m/s
Momentum is conserved: (2.0 kg)(3.0 m/s) = 6.0 kg m/s before, and after the collision the combined 6.0 kg mass moves at 6.0/6.0 = 1.0 m/s. The 1.5 m/s choice divides by the 4.0 kg cart only, ignoring that both carts move together.
Key insight: In a perfectly inelastic collision momentum is still conserved even though kinetic energy is not.
Question 3Intermediate
A 0.060 kg tennis ball approaches a racket at 25 m/s and leaves in the opposite direction at 35 m/s after a contact time of 0.010 s. What is the magnitude of the average force the racket exerts on the ball?
1. A60 N
2. B210 N
3. C360 N
4. D600 N
Show answer
Answer: C. 360 N
Because the ball reverses direction the speeds add: the momentum change is (0.060 kg)(35 + 25) m/s = 3.6 kg m/s, so F = 3.6/0.010 = 360 N. The 60 N choice subtracts the speeds, a sign error that treats the rebound as a slowdown.
Key insight: When an object bounces back, its momentum change is larger than if it simply stopped, because the velocity changes sign.
Question 4Intermediate
A 3.0 kg object at rest on a frictionless surface explodes into two pieces: a 1.0 kg piece that moves off at 6.0 m/s and a 2.0 kg piece. What is the speed of the 2.0 kg piece?
1. A1.5 m/s
2. B3.0 m/s
3. C6.0 m/s
4. D12 m/s
Show answer
Answer: B. 3.0 m/s
Total momentum stays zero, so (1.0 kg)(6.0 m/s) must be balanced by (2.0 kg)v in the opposite direction, giving v = 3.0 m/s. The 12 m/s choice multiplies by the mass ratio instead of dividing by it.
Key insight: In an explosion from rest the two fragments carry equal and opposite momenta, so the heavier piece moves more slowly.
Question 5Advanced
A 0.50 kg glider moving at 2.0 m/s on a frictionless air track collides head-on and elastically with an identical 0.50 kg glider that is at rest. What is the speed of the first glider immediately after the collision?
1. A0 m/s
2. B0.50 m/s
3. C1.0 m/s
4. D2.0 m/s
Show answer
Answer: A. 0 m/s
Conserving both momentum and kinetic energy for equal masses in one dimension requires the gliders to exchange velocities, so the incoming glider stops and the struck glider moves off at 2.0 m/s. The 1.0 m/s choice is the perfectly inelastic result, which would not conserve kinetic energy here.
Key insight: In a one-dimensional elastic collision between equal masses the two objects simply trade velocities.

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Unit 4: Linear Momentum