Question

A body is moving with a velocity $v_0=10m{s}^{-1}.$ It experiences a retardation equal to $0.2v^2.$ Its velocity after $2s$ is given by

• A. $+2m{s}^{-1}$
• B. $+4m{s}^{-1}$
• C. $-2m{s}^{-1}$
• D. $+6m{s}^{-1}$

Answer 1

The correct option is A $+2m{s}^{-1}$

Given, $a=-0.2v^2$
or, $\frac{dv}{dt}=-0.2v^2$
Integrate to get, ${\int }_{10}^v\frac{1}{v^2}dv=-0.2{\int }_0^{2}dt\frac{-1}{v}+\frac{1}{10}=-0.4v=+2m/s$