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 $t=\sqrt{x}+3$, where $x$ is in meter and $t$ is in second. Find the displacement of the particle when its velocity is zero.

Answer 1

$t=\sqrt{x}+3\Rightarrow x=(t-3{)}^2$

$v=\frac{dx}{dt}=2(t-3)=0\Rightarrow t=3s$

$x_{t=3s}=(3-3{)}^2=0$