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**Homework Statement**

A block of mass

*m*=0.75 kg is set on a large cart of mass

*M*= 6.5 kg. The cart's rollers are frictionless, but there is a coefficient of kinetic friction of 0.36 between the cart's surface and the block. The cart is at rest when the block is given an initial speed of 5.2 m/s. The block slides across the cart's surface, but the sliding stops before the block reaches the other end of the cart.

What distance does the cart travel along the floor from the time the block is set in motion to the time sliding ceases?

**The attempt at a solution**

What I did to solve the problem is I first used conservation of momentum to find the final velocity of the cart.

I did mv

_{0}= (m+M)v

_{f}.

Then I found acceleration by doing a = μmg/M.

Then I used those values and used v

^{2}= v

_{0}

^{2}+2ax and solved for x, and got .35 meters, but it is wrong. Can someone help?