A `6 kg` block is kept over a rough surface with coefficient of friction `mu_(s) = 0.6` and `mu_(k) = 0.4` as shown in figure.A time varying force `F = 4t (F` in newton and `t` in second) is applied on the block as shown. Plot a graph between acceleration of block and time `(g = 10 m//s^(2))`

Explanation

`N = mg = 60 N`
`mu_(s) N = 36 N`
`mu_(k) N = 24 N`
Driving force `F = 4t`
Block will move when ,
`F = mu_(s) N` or `4t = 36 rArr t = 9 s`
For `t le 9 s`
`a = 0`
For `t ge 9 s`
At `9 s` block will start moving .Therefore kinetic friction will act `a = (F - mu_(k) N)/(m)`
`= (4t - 24)/(6)`
`= ((2)/(3)t - 4)`
`:. A- 1` graph is a straight time
At `t = 9 s, a = 2 m//s^(2)`
The corresponding `a - 1` graph is an shown in figure .