Question

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

• A. $t^3$
• B. $t^2$
• C. t
• D. $t^{\frac{1}{2}}$

Answer 1

The correct option is B

$t^2$

Given, v = $\alpha$ $\sqrt{x}$

$\frac{dx}{dt}$ = a $x^{\frac{1}{2}}$

$x^{\frac{-1}{2}}$ dx = adt

integrating above equation on both sides

$x^{\frac{1}{2}}$ $\alpha$ at

x $\alpha$ $t^2$