First slide

Rectilinear Motion

Question

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

Moderate

A

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

$\frac{a}{b}$
C

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

zero

Solution

$\begin{array}{l} x = a t^{2} - b t^{3} \\ Velocity = \frac{d x}{d t} = 2 a t - 3 b t^{2} \\ and acceleration = \frac{d^{2} x}{d t^{2}} = 2 a - 6 b t \\ Acceleration will be zero if \\ 2 a - 6 b t = 0 \Rightarrow t = \frac{2 a}{6 b} = \frac{a}{3 b} \end{array}$

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