19. A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12t − t3 . How long would the particle travel before coming to rest?

19. A particle moves along a straight line OX. At a time t (in seconds) the distance x (in metres) of the particle from O is given by \(x = 40 + 12t − t ^3\) . How long would the particle travel before coming to rest?

(a) 40 m

(b) 56 m

(c) 16 m

(d) 24 m

Answer :  (b) 56 m

\( x = 40 + 12t - t^3 \)

\( v = \)\( \frac{dx}{dt} \)\( = 12 - 3t^2 = 0 \)

\( \rightarrow t = 2 \)

\( x_{(t=2)} = 40 + 12(2) - (2)^3 \)

\( = 56 m  \)