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) $\frac{2 a}{3 b}$
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Answer:
Correct Answer: 21.(b)
Solution:
- (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} $