First slide

Rectilinear Motion

Question

Velocity of a particle moving in a straight line varies with its displacement as $v = (\sqrt{4 + 4 s}) m / s$ . Displacement of a particle at time $t = 0 i s s = 0$ . Find displacement of particle at time $t = 2 s .$

Moderate

A

8 m
B

10 m
C

20 m
D

25 m

Solution

Squaring the given equation, we get $v^{2} = 4 + 4 s$ .
Now, comparing it with $v^{2} = u^{2} + 2 a s, we get$
$u = 2 m / s and a = 2 m / s^{2}$
Displacement at $t = 2 s$ is
$s = u t + \frac{1}{2} a t^{2} or s = (2) (2) + \frac{1}{2} (2) (2)^{2} or s = 8 m$

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