Question

A particle moves on the curve $y=\frac{x^4}{4}$ where $x=t/2$, x and y are measured in metre and t in second. At $t=4s$, find the velocity of particle.

Answer 1

$V_y=\frac{dy}{dt}=\frac{dy}{dx}\times \frac{dx}{dt}=x^3\times \frac{1}{2}=\frac{t^3}{16}$

at $t=4^3{V}_y=\frac{4\times 4\times 4}{16}=4m/s{V}_x=\frac{1}{2}m/s$

Velocity of particle is $V=V_x\hat{i}+V_y\hat{j}=\frac{1}{2}\hat{i}+4\hat{j}$