Question

A particle moves under the effect of a force $F=k{x}^2$. Find work done by force when particle displaces from $x=0\text{m}$ to $x=4\text{m}$.

• A. $\frac{8k}{3}$
• B. $\frac{32k}{3}$
• C. $\frac{64k}{3}$
• D. $\frac{128k}{3}$

Answer 1

The correct option is C $\frac{64k}{3}$

Work done by the force $F=k{x}^2$ on a particle from $x=0\text{m}$ to $x=4\text{m}$.
$W=\int F.dxW={\int }_0^{4}k{x}^{2}dxW=k{\left[\frac{x^3}{3}\right]}_0^4=\frac{64k}{3}$