On a stationary block of mass `2kg` a horizontal forces F starts acting at `t = 0` whose veriation with time is shown in figure .The coefficient of friction between the block and ground is `0.5` New answer the following question

Find the time when acceleration of the block is zero

Options

A. At`5s`only
B. At`10s`only
C. Both at`5s and 10s`
D. At a time after `t = 10s `only `5s`only

Answer

c

Explanation

`f_(1) = f_(k) = 0.5 xx 2g = 10 N`
Initialy `F = 20 N gt f_(p)` so the block will start acceleration immeditatelly.
At any time `t : F = 20 - 2r`
Acceleration `a= (20 - 2r - f_(k))/(m) = (10 - 2r )/(m) `...(i)
For ` a = 0,(10 - 2r)/(2) = 0 rArr t = 5s `...(ii)
From Eq (i)`(dv)/(dt) = (10 - 2r)/(2) = 5 - t`
`int _(0)^(v) dv = int _(0)^(1) (5 - t) dt rArr v = 5t - (r^(2))/(2)`
Let us see when the velocity becomes zero for this
`5t - (r^(2))/(2) = 0 rArr t = 10s`
We see that `t = 10s also F = 0` so the block has no tendency to move , hence acceleration is zero `t = 10 s to 15 s` because for this magnitude of `F lt 10 N` so block will remain at rest from `t = 10s to 15s` or acceleration is zero from `10to 15s`