# What exactly happens in a rigid body collision?

Consider a situation in which a body of mass m moving with a velocity v is collided with a similar mass, applying momentum conservation,the initial mass will come to rest and the other mass will move with a velocity of v.

1. Velocity of first mass decreases while the other mass starts accelerating from rest.

2. Both of them reach a common velocity of v/2. How could the mass in the front further accelerate to reach a velocity of v and the mass in back decelerate to zero velocity as there is no relative motion once they attain common velocity?

• When the both velocities are equal, the bodies are still in contact and elastically deformed, so the force is not zero yet. Jan 27, 2021 at 17:11
• Perhaps the animation in this previous answer of mine is of help physics.stackexchange.com/a/541440/93729. Jan 27, 2021 at 17:12
• What you describe is exactly what happens in a completely inelastic collision.
– noah
Jan 27, 2021 at 17:15

Momentum will be exchanged between the bodies (called an impulse). But typically this happens instantaneously for rigid bodies, so there is no in-between state. The total momentum is conserved if an amount $$J$$ is subtracted from one body and added to the other body.
But for deformable bodies, you can approximate the problem with a constant force $$F$$ acting on equal and opposite terms on each body resulting in the change in speed observed after some finite time $$\Delta t$$. The total momentum exchanged is $$J = F \, \Delta t$$, but since the moving body comes to rest, the impulse equals to $$J=m v$$, which is used to find the average force $$F = \frac{m v}{\Delta t}$$