Question

A force $F=5+2x+3x^2$ acts on a particle in $x$ direction where $F$ is in Newton and $x$ is in meter . Find the workdone by this force during a displacement from $x=1\text{m}$ to $x=2\text{m}$.

• A. $15\text{J}$
• B. $12\text{J}$
• C. $32\text{J}$
• D. $-15\text{J}$

Answer 1

The correct option is A $15\text{J}$

Given, variable force $F=5+2x+3x^2$
Workdone by variable force $\left(W\right)={\int }_{x_1}^{x_2}{F}_{x}dxW={\int }_1^2(5+2x+3x^2)dxW=5x{|}_1^2+\frac{2x^2}{2}{|}_1^2+\frac{3x^3}{3}{|}_1^{2}W=5(2-1)+(2^2-1^2)+(2^3-1^3)W=5+(4-1)+(8-1)=15\text{J}$