Question

A body of mass $5\text{kg}$ is acted upon by a variable force which varies with the displacement of the body as shown in figure. What is the speed of the body when it has covered $25\text{m}$? (Assume that the body starts from rest.)

• A. $100\text{m/s}$
• B. $10\text{m/s}$
• C. $25\text{m/s}$
• D. $20\text{m/s}$

Answer 1

The correct option is B $10\text{m/s}$

The body starts from rest $v_1=0$, Let the speed of the body after covered $25\text{m}$ is $v_2$.

By the work energy theorem, Change in kinetic energy $=$ Net work done$\left(W\right)$

$W=$ Area under $F-S$ curve till $25\text{m}$
$=10\times 25=250\text{J}$

$\Rightarrow \frac{1}{2}m(v_2^2-v_1^2)=250$
$\frac{1}{2}\times 5\times \left(v_2^2\right)=250$ ($\therefore v_1=0$)
$v_2^2=100$
$v_2=10\text{m/s}$

Hence option B is the correct answer