Question

A particle moves along a straight line OX. At a time t (in second) the distance x of the particle from O 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

Answer: (C)

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