First slide

Instantaneous acceleration

Question

The position x of a particle varies with time t as $x = {at}^{2} - {bt}^{3}$ .The acceleration of the particle will be zero at time t equal to

Moderate

A

$\frac{a}{b}$
B

$\frac{2 a}{3 b}$
C

$\frac{a}{3 b}$
D

Zero

Solution

$\frac{dx}{dt} = 2 at - 3 {bt}^{2} \Rightarrow \frac{d^{2} x}{{dt}^{2}} = 2 a - 6 bt = 0 \Rightarrow t = \frac{a}{3 b}$

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