Question

Force versus displacement curve is shown in the diagram. Find the final velocity of the particle of mass $5\text{kg}$ at the end of $30\text{m}$, if it is moving initially with $2\text{m/s}$.

• A. $10\text{m/s}$
• B. $5.23\text{m/s}$
• C. $4.89\text{m/s}$
• D. $7.64\text{m/s}$

Answer 1

The correct option is C $4.89\text{m/s}$

Let final velocity after $s=30\text{m}$ is $v_2$
Given initial velocity $v_1=2\text{m/s}$

According to work energy theorem
Net work done $=$ Change in kinetic energy

$\Rightarrow$ Change in kinetic energy $=$ Area under $F-S$ curve (till $30\text{m}$)
Area of tringle $OAB$ $-$ Area of tringle $BCD$

$=\frac{1}{2}\times 20\times 10-\frac{1}{2}\times 10\times 10=50\text{J}$
$\frac{1}{2}m(v_2^2-v_1^2)=50\text{J}$
$\Rightarrow \frac{1}{2}\times 5\times (v_2^2-4)=50\text{J}$
$\Rightarrow v_2=4.89\text{m/s}$

Hence option C is the right answer.