Question

A force $$F=\alpha +bx$$  acts on a particle in the x-direction, where a and b are constants. Find the work done by this force during a displacement from x = 0 to x = d. 

 

 

Answer 1

Given that force is a function of displacement, i.e.

$$F=a+bx$$ ,

where a and b are constants.
So, work done by this force during the displacement x = 0 to x = d,

$$W=\underset{0}{\overset{d}{\int }}F\text{ dx }$$
$$W=\underset{0}{\overset{d}{\int }}(a+bx)dx$$
$$W={[ax+\frac{b{x}^2}{2}]}_0^d$$
$$W=ad+\frac{b{d}^2}{2}$$
$$\Rightarrow W=(a+\frac{bd}{2})d$$