Question

For the force-displacement graph for a particle is as shown below. If the particle has mass of $2\text{kg}$ and has initial velocity of $2\text{m/s}$, calculate final kinetic energy of particle, when it displaces from $x=1\text{m}$ to $x=5\text{m}$.

• A. $24\text{J}$
• B. $10\text{J}$
• C. $30\text{J}$
• D. $0\text{J}$

Answer 1

The correct option is A $24\text{J}$

According to work energy theorem we know that,
Change in kinetic energy $=$ Net work done.

We also know that net work done is
$=$ Area under $F-S$ curve

$=$Area of part $I+$Area of part $II-$Area of part $III+$ Area of part $IV$

$=(10\times 1)+(20\times 1)-(20\times 1)+(10\times 1)$
$=20\text{J}$

Hence the change in kinetic energy
$K_f-K_i=20\text{J}$
Given $m=2\text{kg},u=2\text{m/s}$
then $K_i=\frac{m{u}^2}{2}=4J$
$\Rightarrow K_f-4=20\text{J}$
$\Rightarrow K_f=24\text{J}$
Option A is the correct answer