First slide

Rectilinear Motion

Question

Particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity v that varies as $v = a \sqrt{x}$ . The displacement of the particle varies with time as

Moderate

A

t³
B

t²
C

t
D

t ^1/2

Solution

Velocity, $\frac{dx}{dt} = a \sqrt{x} or \frac{dx}{\sqrt{x}} = adt$
Integrating it, we have
$\int x^{- 1 / 2} dx = \int adt$
or $2 x^{1 / 2} = at or x \propto t^{2}$

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