# What will happen when a cart moving on a horizontal track collides with a cart of the same mass that is at rest? [closed]

Our teacher gave us several options, but the only ones that don't violate conservation of momentum are:

Cart A and Cart B move together with the same velocity

Car A and Car B move with Car B having a greater velocity than Car A

Car A stops and Car B moves with the same velocity that Car A had before the collision

The third option is the only one that definitely does not violate conservation of momentum, the other two options could either violate it or not violate it. Can anyone explain what happens in this situation and why? We are told that rolling friction is negligible here and should be ignored.

For simplicity I'm assigning mass $$2kg$$ to each and initial velocity of the moving cart to be $$2ms^{-1}$$.You can find particular cases for all your options where momentum will be conserved , suppose both carts stick and move with velocity $$1ms^{-1}$$ , and obviously the last option also conserves momentum, so you need more data to determine the end result of the collision , here comes the use of coefficient of restitution ,it is an experimentally determined quantity which is nothing but the ratio of relative velocities of separation and approach , for elastic collision , the ones in which kinetic energy is also conserved its value is 1.You can now obtain a second relation from this data which will help you determine velocities after collision and conclude the last option to be correct.