In a smooth stationary cart of length d, a small block is projected along it's length with velocity v towards front. Coefficient of restitution for each collision is e. The cart rests on a smooth gsround and can move freely. The time taken by block to come to rest w.r.t. cart is:
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Between each collision the block moves a distance d relative to cart.
Initial relative velocity v
Coefficient of restitution, e = relative speed after collision/relative speed before collision
Relative velocity after 1 collision 
ve
In general. Relative velocity after n collisions 
So, total time when relative velocity becomes 
whered 
for each round of collision and 
Time total 
infinite
since the series is diverging as 
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