Question

The force applied on a moving object with a mass of `5 kg` on a linear path is given by `F(x)=x^2+1`. How much work would it take to move the object over `x in [1,4 ]`?

Answer 1

I got: `24J`

Explanation:

As we have a variable force I would use the integral form of work as:

`W=int_(x_1)^(x_2)F(x)dx=`

In your case:

`W=int_1^4(x^2+1)dx=x^3/3+x|_1^4=`
`=(4^3/3+4)-(1^3/3+1)=(64+12-1-3)/3=24J`