A particle located at x = 0, at time t = 0 starts moving along the positive x

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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 = $α$ $\sqrt{x}$ .The displacement of the particle varies with time as

Options:

A .

t^{3}

B .

t^{2}

C . t

D .

t^{\frac{1}{2}}

Answer: Option B
:
B

Given, v = $α$ $\sqrt{x}$

$\frac{d x}{d t}$ = a $x^{\frac{1}{2}}$

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

integrating above equation on both sides

$x^{\frac{1}{2}}$ $α$ at

x $α$ $t^{2}$

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