Question

A force $F_x$ acts on a particle such that its position $x$ changes as shown in figure.
The work done by the particle as it moves from $x=0$ to $20m$ is

• A. $37.5J$
• B. $10J$
• C. $15J$
• D. $22.5J$
• E. $45J$

Answer 1

The correct option is E $45J$

Key Concept As, we know, work done by a variable force, $W_{n_i\to n_t}$
$=$ area under the force $-$ displacement curve.
Work $=$ Area of $△ABF+$ Area of $△BCEF+$ Area of $△ECD$
Work done by the particle as it moves from $n=0$ to $20m$,
$W=\frac{1}{2}\times 3\times 5+10\times 3+\frac{1}{2}\times 5\times 3$
$\Rightarrow W=\frac{15}{2}+30+\frac{15}{2}$
$\Rightarrow W=15+30=45J$.