Question

A particle moves along a straight line OX. At a time t (in second) the distance x of the particle from 0 is given by $x=40+12t-t^3$. How long would the particle travel before coming to rest ?

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

Answer 1

The correct option is C 56 m

Distance travelled by the particle is
$x=40+12t=t^3$
$v=\frac{dx}{dt}=12-3t^2$
But final velocity v=0
$12-3t^2=0$
$t^2=\frac{12}{3}=4$
$t=2s$
$x=40+12\left(2\right)-8=56m$