Question

A variable force $F=3x^2$ is applied on an object. What is the work done to move the object from x = 0m to x = 5m?

(Assume the displacement is in the direction of force applied at all points)

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Answer 1

We know that work done by force f(x) is given by W = $\int$ f(x) dx , when the displacement is in the direction of force.

So,

work done = $\int 3x^{2}dx$

Using the formula $\int x^{n}dx=\frac{x^{n+1}}{n+1}$, we get

$W\left(x\right)=x^3+C$

Work done when x= 0 is zero.

$\Rightarrow W\left(0\right)=0$

$\Rightarrow C=0$

We want to find W(5)

$W\left(5\right)=5^3$

= 125