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A particle moves along a straight line O...

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

24m

B

40m

C

56m

D

16m

Text Solution

Verified by Experts

The correct Answer is:
D
`x = 40 + 12t - t^3`
`v = (dx)/(dt) = 12 - 3t^2`
final velocity v = 0
rArr `3t^2 = 12 rArr t = 2 sec
` therefore x = 40 + 12 xx 2 - (2)^3 = 56m`
` x = 56-40`
= 16m
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