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. 40m
B. 56m
C. 16m
D. 24m

Answer

B

Explanation

`x= 40 + 12t- t^(3)`
`v= (dx)/(dt) = 12 - 3t^(2)`
For `v=0, t= sqrt((12)/(3)) = 2 sec`
So, after 2 seconds velocity becomes zero.
Value of x in 2 secs `= 40 + 12 xx 2- 2^(3) = 40 + 24 - 8 = 56m`