First slide

Instantaneous velocity

Question

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

Easy

A

t^1/2
B

t³
C

t²
D

t

Solution

Given $v = α \sqrt{x} or (dx / dt) = α \sqrt{x}$
Integrating, we get
$\begin{array}{l} \int_{0}^{x} \frac{dx}{\sqrt{x}} = α \int_{0}^{t} dt \\ ∴ 2 \sqrt{x} = αt \end{array}$
or $x = \frac{α^{2} t^{2}}{4} \propto t^{2}$

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