Question

A position dependent force $F$ is acting on a particle and its force position curve is shown in the figure. Change in kinetic energy of the particle, when its displacement is from $0$ to $5\text{m}$ is

• A. $5\text{J}$
• B. $10\text{J}$
• C. $15\text{J}$
• D. $20\text{J}$

Answer 1

The correct option is A $5\text{J}$

By the work energy theorem, Change in kinetic energy $=$ Work done

Work done $=$ Area under $F-S$ curve
$\Rightarrow W=$ Area (trapezium $ABCD$) $-$ Area (trapezium $DFJI$)

We know that area of trapezium is given by, $\frac{1}{2}\times \left(\text{sum of opposite side}\right)\times \text{height}$

$=\frac{1}{2}\times (3+1)\times 10-\frac{1}{2}\times (2+1)\times 10$
$=20-15=5\text{J}$

Hence option A is the correct answer.