Question

A varying force is given as
$F=\left\{\begin{array}{cc}4\text{N}& 0\le x\le 6\\ 6x\text{N}& 6<x\le 10\\ 3x^2\text{N}& 10<x\le 20\end{array}\right\}$ (where $x$ is meters)
Find the total work done by this force to displaces from $x=4$ to $x=15$ metres.

• A. $0$
• B. $2000\text{J}$
• C. $2500\text{J}$
• D. $2575\text{J}$

Answer 1

The correct option is D $2575\text{J}$

Work done by variable force $W=\underset{a}{\overset{b}{\int }}F.dx$
Here, $a=4$ and $b=15$
$W=\underset{4}{\overset{15}{\int }}F.dx$
$=\underset{4}{\overset{6}{\int }}F.dx+\underset{6}{\overset{10}{\int }}F.dx+\underset{10}{\overset{15}{\int }}F.dx$
$=\underset{4}{\overset{6}{\int }}4dx+\underset{6}{\overset{10}{\int }}6xdx+\underset{10}{\overset{15}{\int }}3x^{2}dx$
$=4[x{]}_4^6+\frac{6}{2}[x^2{]}_6^{10}+[x^3{]}_{10}^{15}$
$=4[6-4]+3[100-36]+[3375-1000]$
$=8+192+2375$
$=2575\text{J}$