Question

A body starts moving with a velocity $v_0=10{ms}^{-1}$. It experiences a retardation equal to $\frac{1}{5}{v}^2$. Its velocity after $2s$ is given by

• A. $-3.33{ms}^{-1}$
• B. $+4{ms}^{-1}$
• C. $+3.33{ms}^{-1}$
• D. $+6{ms}^{-1}$

Answer 1

The correct option is A $-3.33{ms}^{-1}$

Retardation $a=-\frac{v^2}{5}$

Or $\frac{dv}{dt}=\frac{-v^2}{5}$

Or ${\int }_{10}^v{v}^{-2}dv={\int }_0^2\frac{dt}{5}$

Or $-\frac{1}{v}{|}_{10}^v=\frac{t}{5}{|}_0^2$

Or $\frac{1}{10}-\frac{1}{v}=\frac{2}{5}$

$⟹v=\frac{-10}{3}m/s$