Question

A particle of mass $m$ initially moving with speed $v$. A force acts on the particle $f=kx$ where $x$ is the distance travelled by the particle and $k$ is constant. Find the speed of the particle when the work done by the force equals $W$.

• A. $\sqrt{\frac{k}{m}+v^2}$
• B. $\sqrt{\frac{2W}{m}+v^2}$
• C. $\sqrt{\frac{2W}{k}+v^2}$
• D. $\sqrt{\frac{W}{2m}+v^2}$

Answer 1

The correct option is B $\sqrt{\frac{2W}{m}+v^2}$

Given,

Final velocity, $v_1$

Change in kinetic Energy = work done by force

$\frac{1}{2}m{v}_1^2-\frac{1}{2}m{v}^2=W$

$v_1=\sqrt{\frac{2W}{m}+v^2}$

Hence, final velocity is $\sqrt{\frac{2W}{m}+v^2}$