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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
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B
40 m
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C
56 m
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D
16 m
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Solution

The correct option is C 56 m
Distance 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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