15. The displacement of a particle varies with time (t) as: s = at2 − bt3 . The acceleration of the particle will be zero at time t equal to

15. The displacement of a particle varies with time (t) as: \( s = at^2 − bt^3 \) . The acceleration of the particle will be zero at time t equal to

(a)  \( \frac{a}{b} \)

(b)  \( \frac{a}{3b} \)

(c)  \( \frac{3b}{a} \)

(d)  \( \frac{2a}{3b} \)

Answer :  (b)  \( \frac{a}{3b} \)

\( \large s = A t^{\Large 2} - B t^{\Large 3} \)

\( \large v = \frac{\Large dS}{\Large dt} = 2A t - 3B t^{\Large 2} \)

\( \large a = \frac{\Large dV}{\Large dt} = 2A - 6B t = 0 \)

\( \large t = \frac{A}{3B} \)