Is My Solution to This Force/Friction Physics Problem Correct?

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The discussion focuses on a physics problem involving two blocks, where a horizontal force is applied to a smaller block on top of a larger block. The user presents their calculations for the accelerations of both blocks and the time required for the smaller block to slide off the larger one. They derive the equations for the frictional force and the accelerations, concluding with a formula for time based on the distance L and the accelerations a1 and a2. The calculations appear to be logically structured, but verification from others is sought to confirm their accuracy. The solution is presented clearly, indicating a solid understanding of the physics concepts involved.
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Can someone check if I did this problem right?

A horizontal force F is applied to a small block of mass m1 to make It slide along the top of a larger block of mass m2 and length L. The coefficient of friction between the blocks is \mu. The larger block slides without friction along a horizontal surface. The blocks start from rest with the small block at one end of the larger block.

a) Find the acceleration of each block. a1 and a2, relative to the horizontal surface.

b) In terms of L, a1, and a2, find the time t needed for the small block to slide off the end of the larger block.

This is what I did. f is friction, F is the applied force

a)

f = F - m1a1
f = m2a2
f = \mum1g

\mum1g = F - m1a1
a1 = (F - \mum1g) / m1
a2 = \mum1g/m2
b)

L = .5(a1 - a2)t2

t = \sqrt{2L / (a1 - a2)}
 
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Looks good to me.
 

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