Skip to content
GRE Physics overview

Public question explainer

Original public content

Perfectly Inelastic Collision: Public Worked Question

A public momentum question showing how to find the shared final speed after two carts couple in a perfectly inelastic collision.

Question

On a frictionless track, a 3.0 kg3.0\,\text{kg} cart moving at 4.0 m/s4.0\,\text{m/s} collides with a stationary 1.0 kg1.0\,\text{kg} cart and the two couple together. What is the speed of the coupled carts just after the collision?

  1. a.12 m/s12\,\text{m/s}
  2. b.4.0 m/s4.0\,\text{m/s}
  3. c.3.0 m/s3.0\,\text{m/s}
  4. d.2.0 m/s2.0\,\text{m/s}

Correct answer

C. 3.0 m/s3.0\,\text{m/s}

Full reasoning

  1. 1Compute the initial momentum: pi=(3.0)(4.0)+(1.0)(0)=12 kg⋅m/sp_i = (3.0)(4.0) + (1.0)(0) = 12\,\text{kg}\cdot\text{m/s}.
  2. 2The carts couple, so they share one final velocity and the combined mass is 3.0+1.0=4.0 kg3.0 + 1.0 = 4.0\,\text{kg}.
  3. 3Conservation gives vf=pi/(m1+m2)=12/4.0=3.0 m/sv_f = p_i/(m_1 + m_2) = 12/4.0 = 3.0\,\text{m/s}.
  4. 4Kinetic energy is not conserved here — some is lost in the coupling — but momentum is.

Why each choice is right or wrong

Choice A

This is the numerical value of the system momentum, 12 kg⋅m/s12\,\text{kg}\cdot\text{m/s}, reported as a speed without dividing by the combined mass.

Choice B

This divides the total momentum by the incoming cart's 3.0 kg3.0\,\text{kg} alone, forgetting that the coupled pair has 4.0 kg4.0\,\text{kg} of mass.

Choice C

Correct. Momentum conservation gives vf=(3.0)(4.0)/(3.0+1.0)=12/4.0=3.0 m/sv_f = (3.0)(4.0)/(3.0 + 1.0) = 12/4.0 = 3.0\,\text{m/s}.

Choice D

This averages the two initial speeds, (4.0+0)/2(4.0 + 0)/2, which ignores the unequal masses of the carts.

Related formula

Momentum conservation for a perfectly inelastic collision

m1v1+m2v2=(m1+m2)vfm_1v_1 + m_2v_2 = (m_1 + m_2)v_f

Assumptions: External horizontal forces are negligible during the collision. The carts move together after impact.

Related topic and practice

Energy and Momentum ConservationSign in for current practice

This public explainer is separate from the protected practice bank. Current practice coverage varies.

Source and public-release record

Authored for this public explainer registry. It has no database question ID and is not copied from a protected or official exam bank.

  1. University Physics Volume 1, Section 9.4: Types of Collisions — OpenStax. Accessed 2026-08-02. OpenStax textbook content is CC BY-NC-SA 4.0; attribute and avoid verbatim reuse beyond short cited references.

Review and maintenance

Source-checked by publisher
Publisher record
Keiko Study editorial owner
Publisher placeholder; no individual credential claim is made yet.
Reviewer record
Technical reviewer pending
Placeholder only; this content is not labeled as reviewed by a named specialist.
Last source check
2026-08-07
Next scheduled review
2026-11-07

Recheck the cited OpenStax reference before each major GRE Physics preparation cycle.

Report an issue with this page