If I have two objects colliding with equal mass it could be that the object exerting the force on the other (object A) comes to rest while the other (object B) is accelerated to the initial speed of object A. However could it also be that object A exerts a smaller force on B, not coming fully to rest, while object B is not fully accelerated to the initial speed of A.
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Do you want to know about force or about the resulting behavior of the objects? What's your question? – Bill N Apr 01 '21 at 14:22
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Does this answer your question? What factors indicates inelastic collision? – Sandejo Apr 02 '21 at 21:34
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Sure. For example, in a perfectly inelastic collision the velocities of A and B after the collision will both be equal to half the original velocity of A.

gandalf61
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But how to determine whether object B will accelerate to only half the velocity or whether it will accelerate to the initial velocity of A. Is there a way to tell before they collide? – Aliska Apr 01 '21 at 13:35
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@Aliska That's a different question. If you want the PSE community to consider it, you should make another question post, not a comment. – Bill N Apr 01 '21 at 14:21
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@Aliska The relative velocities of A and B after the collision are determined by the coefficient of restitution between the objects. The coefficient of restitution is $0$ for a perfectly inelastic collision and $1$ for a perfectly elastic collision, but can take any other value between $0$ and $1$. See https://en.wikipedia.org/wiki/Coefficient_of_restitution for more details. – gandalf61 Apr 01 '21 at 14:24