A force `F=(2+x)` acts on a particle in x-direction where F is in newton and x in metre. Find the work done by this force during a displacement form 1. 0 m to x = 2.0 m.

Explanation

As the force is variable, we shall find the work done in a small displacement from x to x+dx and then integrate it to find the total work. The work done in this small displacement is
dW = Fdx=(2+x)dx
Thus, `" " W=int_(1)^(2) dW =int_(1)^(2)(2+x)dx`
`=[2x+(x^(2))/(2)]_(1)^(2)=[(4+(4)/(2))-(2+(1)/(2))]=3.5 J`