Question

The distance $x$ of a particle moving in one-direction, under the action of a constant force is related to time by equation
$t=\sqrt{x}+3$
where $x$ is in metres, $t$ is in seconds.
Find the displacement of the particle when its velocity is zero.

Answer 1

The equation of time is given as,

$t=\sqrt{x}+3$

$\sqrt{x}=t-3$

$x=t^2-6t+9$

The velocity is given as,

$\frac{dx}{dt}=2t-6$

When the velocity is zero, it can be written as,

$0=2t-6$

$t=3$

The displacement at $3s$ is given as,

$x=3-3$

$x=0$

Thus, the displacement of the particle is zero, when its velocity is zero.