The masses of the block A and B are `m and M` Between A and B there is a constant force `F` but B can slide frictionlessly on the horizontal surface A is set in motion with velocity `v_(0)` while B is at rest . What is the distance moved by A relative to B before they move with the same velocity

Answer

` (m +Mv_(0)^(2))/(m+5m+2 mu m)s `

Explanation

The same frictional force is effective an A and B .This force produces retardation ao A and acceleration on B till they acquire a common velocity
`F = ma = Ma'`
where a is the absolute reterdation m,a' is the absolute acceleration of `M`
Relative retardation of `m= a - (-a') = a + a'`
initial relative velocity `= v_(0)`
Final relative velocity` = 0`
`:. v_(0)^(2) = 2(a + a)a `
where s is the direction covered by `m` relative to `M`
or `v_(0)^(2) = 2 ((F)/(m) + (F)/(M)) s= (2F(m +M))/(mM)s `
or `s = (mMv_(0))/(2F(m + M))`