Question

A less massive moving object has an elastic collision with a more massive object that is not moving. Compare the initial velocity of the less massive object to it's final velocity

Answer 1

Assume that the small-massed particle is $m$ and the heavier mass particle is $M$.

Now, by momentum conservation and energy conservation:

   $mv = mv_{m} + Mv_{M}$

   $mv^{2} = mv^{2}_{m} + Mv^{2}_{M}$

Now, there are 2 solutions but, one of them is useless to this question's main point so I excluded that point. Ask me in the comments if you want the excluded solution too.

   $v_{m} = v\frac{m - M}{m + M}\\\\\\v_{M} = v\frac{m + M}{m + M}$

So now, we see that $v_{m} < 0$ and $v_{M} > 0$. So therefore, the smaller mass recoils out.

Hope this helps you!

Bye!