Question

The force applied on a moving object with a mass of `3 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 [0,2 ]`?

Answer 1

I found: `W=14/3J`

Explanation:

Having a variable force I would use the work in integral form as:
`W=int_(x_1)^(x_2)F(x)dx` along `x`.
We have:
`W=int_0^2(x^2+1)dx=`
Solve it as usual:
`=int_0^2(x^2+1)dx=x^3/3+x=`
Apply the extremes:
`=(2^3/3+2)-(0^3/3+0)=8/3+3=(8+6)/3=14/3`
so we get:
`W=14/3J`