Question

Solve this:
The displacement of a particle is zero at time = 0 and is x at time = t. It starts moving in the positive x-direction with a velocity which varies as v = k$\sqrt{x}$ where k is a constant. Show that velocity is directly proportional to time.

Answer 1

$$\begin{gathered} Dearstudent, \\ v=k\sqrt{x} \\ \sin cev=\frac{dx}{dt}also, \\ \frac{dx}{dt}=k\sqrt{x} \\ \frac{dx}{\sqrt{x}}=kdt \\ 2\sqrt{x}=kt \\ x=\frac{k^2{t}^2}{4} \\ Henceprovedvelocityisdirectlyproportionaltotimeasdisplacementisproportionalalso. \\ Regards \end{gathered}$$