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 √ x . The displacement of the particle varies with time as Options: A . &nbsp t 3 B . &nbsp t 2 C . &nbsp t D . &nbsp t 1 2

Answer: Option B : B Given, v = α √ x d x d t = a x 1 2 x − 1 2 dx = adt integrating above equation on both sides x 1 2 α at x α t 2

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

Discussion Forum : Motion In One Dimension

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 = $α$ $\sqrt{x}$ .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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