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Mass A is initially moving with a velocity of 24 m/s in the +x-direction. Mass B is twice as massive as mass A and is initially at rest. The two objects experience a totally inelastic collision. What is the final speed of both objects after the collision?
  1. A is not moving; B is moving 24 m/s in the +x-direction.
  2. Neither A nor B is moving.
  3. A is moving 24 m/s in the –x-direction. B is not moving.
  4. Both A and B are moving together 8 m/s in the +x-direction.
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OpenStax College Physics for AP® Courses Solution, Chapter 8, Problem 47 (Test Prep for AP® Courses) (1:25)

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This is College Physics Answers with Shaun Dychko. We have mass B is two times mass A, so when we write our conservation of momentum formula we can just write the letter m with no subscript because the first mass will be <i>m</i> and the second mass will be two <i>m</i>. So we have the total momentum initially is <i>m vA</i> plus two <i>m</i> times <i>vB</i> although this term is zero because mass B is initially at rest. Then after the collision the two objects stick together so there is a single thing of mass <i>m</i> plus two <i>m</i> and it has some speed <i>v prime</i> that we're going to find. So because this term became zero, this conservation of momentum equation reduces to <i>m vA</i> equals three <i>m v prime.</i> So we divide both sides by three <i>m</i> to solve for <i>v prime</i>. That means -- well, actually I guess it's just solve for -- I guess I did this in two steps didn't I? Well, it doesn't really matter. Yeah, so divide both sides by <i>m</i> and you get this and then divide both sides by three. You get <i>v prime</i> is <i>vA</i> over three. So that's 24 meters per second is the initial velocity of mass A and one third of that is eight meters per second. So the answer is D, they're both moving together eight meters per second in a positive direction because this is positive eight meters per second.