Question

A force $F$ acting on a particle varies with the position $x$ as shown in the graph. Find the work done by the force in displacing the particle from $x=-a$ to $x=+2a$.

• A. $\frac{3ab}{2}$
• B. $\frac{4ab}{2}$
• C. $\frac{2}{3ab}$
• D. $\frac{2}{4ab}$

Answer 1

The correct option is A $\frac{3ab}{2}$

$x=-a$ to $x=+2a$

Average force $=\frac{-b+2b}{2}=\frac{b}{2}$

$W={\int }_{-a}^{2a}Fdx$

$={\int }_{-a}^{2a}\frac{b}{2}dx$

$W=\frac{b}{2}[x{]}_{-a}^{2a}$

$=\frac{b}{2}[2a+a]$

$=\frac{3ab}{2}$