First slide

Rectilinear Motion

Question

The displacement of a particle is proportional to the cube of the time. Then magnitude of its acceleration

Moderate

A

Decreases with time
B

zero
C

Increases with time
D

Constant

Solution

Given that $S α t^{3}$
velocity $V = \frac{d s}{d t}$
$\begin{matrix} \begin{aligned} = \frac{d}{d t} (t^{3}) \\ \Rightarrow V α 3 t^{2} \end{aligned} \\ ∴ acceleration a = \frac{d v}{d t} \\ = \frac{d}{d t} (3 t^{2}) \\ \Rightarrow a α 6 t \end{matrix}$
$\Rightarrow a α t$

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