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Perfectly Inelastic Collision

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 ConservationClassical Mechanics Domain GuideA collision that conserves momentum but loses kinetic energyEnergy Conservation on a Frictionless TrackNewton's Second Law and Free-Body DiagramsSimple Harmonic MotionCreate a free account to practice

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Sources

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.
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Sources last checked 2026-08-07

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