Motion In A Straight Line Ques 21

21. The displacement of a particle varies with time (t) as: $s=a t^{2}-b t^{3}$. The acceleration of the particle will be zero at time $t$ equal to

[1997]

(a) $\frac{a}{b}$

(b) $\frac{a}{3 b}$

(c) $\frac{3 b}{a}$

(d) $\frac{2 a}{3 b}$

Show Answer

Answer:

Correct Answer: 21.(b)

Solution:

  1. (b) distance, $s=a t^{2}-b t^{3}$

velocity, $v=\frac{d s}{d t}=2 a t-3 b t^{2}$

acceleration $a=\frac{d v}{d t}=2 a-6 b t$

Acceleration is zero at

$ 2 a-6 b t=0 \Rightarrow t=\frac{a}{3 b} $