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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 ?

A

24 m

B

40 m

C

56 m

D

16 m

Text Solution

Verified by Experts

The correct Answer is:
D
`x=40+12t-t^(3)`
Speed `(dx)/(dt)=0+12-3t^(2)rArr t= +- 2`sec
`:. x(2)=40+12xx2-2^(3)`
`=64-8=56 m`
at `t=0, x(0)=40`
`Deltax=x(2)-x(0)=16`
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