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 metre and t in second. Calculate the velocity at any $t$.

Answer 1

As $t=\sqrt{x}+3$

i.e., $x={(t-3)}^2$

So, $v=\frac{dx}{dt}=2(t-3)$