Physics problem using Newton's laws and kinematics?

Question

Consider a small block sitting atop a much more massive block. There is some friction between the two blocks (call it μ sub 0). However, the bottom block sits on a frictionless surface. Initially the two blocks are at rest. Someone then gives the top block a push until it begins moving at a speed. At this point no further external forces are applied.

We observe that the small block begins to slow down and the large block begins to speed up. Explain why this happens (what forces are responsible), and write down expressions for velocity versus time for the 2 blocks. Compare both forces and accelerations on the 2 blocks. Then find the time it takes before the 2 blocks reach the same speed relative to the ground.

Answer 1

When the external force ceases to be applied, the top block has momentum. Let's call this moment t=0, and the speed of the top block at that moment v0. The only horizontal force acting on the top block is friction between it and the lower block inhibiting its speed. Therefore it will decelerate according to
m*a=-m*g*μ0
or a=-g*μ0

so the velocity of the top block is
v(t)=v0-g*μ0*t


The only horizontal force acting on the lower block is the friction accelerating the block. At t=0, it's speed is vL0
and
vL(t)=VL0+g*μ0*t

when v(t)=vL(t), the blocks will move together and friction will prevent them from separating

v0-g*μ0*t=VL0+g*μ0*t
t=(v0-VL0)/(2*g*μ0)

j