Question

The force applied on a moving object with a mass of `1 kg` on a linear path is given by `F(x)=2x +3`. How much work would it take to move the object over `x in [1,3]`?

Answer 1

`14 J`

Explanation:

It is necessary to know what unit are using for the force and distance. We can guess that they are Newtons and metres, respectively.

As force depends on the position we should use the integral form of work

`W = int_a^b F(x) dx` and in our particular problem

`W = int_1^3 (2*x+3) dx = x^2]_1^3 +3*x]_1^3 = 14J`

The mass is not important because the work is independent on it if the force is fixed. For similar force, similar work, for different mass, different speed but this question was not in this problem.