A long plank begins to move at `t=0` and accelerates along a straight track wit a speed given by `v=2t^(2)` for `0le t le 2` (where `v` is in m/s and `t` is in second). After 2 sec the plane continues to move at the constant speed acquired. A small initially at rest on the plank begins to slip at `t=1` sec and stops sliding at `t=3` sec. If the coefficient of static friction and kinetic friction between the plank and the block is `0.s` and `0.k` (where `s` and `k` are digits) respectively, find `s+k` (take `g=10m//s^(2)`)

Answer

7

Explanation

`mu_(s)g= (dv)/(dt)` at `t=1` sec
`:. mu_(s)=0.4`
At `t=3` sec velocities of plank and block are equal.
`:.2+mu_(k)g(2)=v` at `t=3` sec `=8`
`:.mu_(k)=0.3`
`:.s+k=4+3=7`