Question

The displacement x of a particle moving along x-axis at time t is given by x square is equals to 2 t square + 60 the velocity at any time t is

Answer 1

The velocity of particle X at time t will be
$\frac{4t}{2 \sqrt{2 {t}^{2} + 60 } }$

Answer 2

Answer: The velocity at any time t is $v = \dfrac{2t}{\sqrt{2t^{2}+60}}$.

Explanation:

Given that,

Displacement $x^{2}=2t^{2}+60$

$x = \sqrt{2t^{2}+60}$

We know that,

The velocity is the rate of change of displacement.

The velocity is

$v = \dfrac{dx}{dt}$

$v = \dfrac{d}{dt}(\sqrt{2t^{2}+60})$

$v = \dfrac{1}{2}(2t^{2}+60)\times 4t$

$v = \dfrac{2t}{\sqrt{2t^{2}+60}}$

Hence, the velocity at any time t is $v = \dfrac{2t}{\sqrt{2t^{2}+60}}$.