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

Solution

## The correct option is C 56 mDistance travelled by the particle is$$x=40 +12 t=t^3$$$$v=\dfrac {dx}{dt} =12-3t^2$$But final velocity v=0$$12-3t^2=0$$$$t^2 =\dfrac {12}{3}=4$$$$t=2s$$$$x=40 +12 (2) -8 =56 m$$Physics

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