A particle moves along a straight line `OX`. At a time `t` (in seconds) the distance `x` (in metre) of the particle is given by `x = 40 +12 t - t^3`. How long would the particle travel before coming to rest ?

Options

A. 16m
B. 21m
C. 40m
D. 56m

Answer

D

Explanation

`x=40+12t-t^(3)`
`(dx)/(dt)=0+12-3t^(2)`
`v=12-3t^(2)`,
When velocity is zero (body at rest)
`12-3t^(2)=0`
`t^(2)=4`
`t=+2,-2`
Only positive time is taken `therefore t=2` s
The distance travelled by particles belive coming to rest in tie t=2 seconds is
`x=40+12(2)-2^(2)`
`=40+24-8`
=56m