First slide

Rectilinear Motion

Question

The position $' y'$ of a particle varies with time (t) as $y = a t^{3} - b t^{2}$ . The acceleration at time of the particle will be equal to zero, where ‘t’ is equal to

Moderate

A

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

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

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

$\frac{a}{3 b}$

Solution

$\begin{aligned} \begin{aligned} Given that y = a t^{3} - b t^{2} \\ ∴ Velocity V = \frac{d y}{d t} \\ = 3 a t^{2} - 2 b t \end{aligned} \\ acceleration a = \frac{d v}{d t} \\ = 6 a t - 2 b \\ \begin{array}{c} ∴ If a = 0 i.e \\ \begin{array}{l} 6 a t - 2 v = 0 \\ \Rightarrow 6 a t = 2 b \\ \Rightarrow t = \frac{2 b}{6 a} = \frac{b}{3 a} \end{array} \end{array} \end{aligned}$

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