Question

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

Answer 1

Given $t-3=\sqrt{x}⟹\sqrt{x}=t-3⟹x=(t-3{)}^2=t^2-6t+9$
Therefore, the velocity of the particle is
$v=\frac{dx}{dt}=2t-6$
and it will be zero when
$2t-6=0⟹t=3s$
Hence, the velocity of the particle will be zero when t = 3 s. Putting t = 3 s. in (1), we get the required displacement of the particle as
$x=3^2-6\times 3+9=0$
$⟹x=0$