Question

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

Answer 1

I found `6.7J`

Explanation:

I think we would need at least an equal force to keep on moving the object as the one opposing it (at least without accelerating it maintaining a constant velocity)..
Here we have a variable force (depending on `x`) so we need to use the integral form for Work as:
`W=int_(x_1)^(x_2)F(x)dx`
or in our case:
`W=int_1^2(2+e^x)dx=`
let us solve it:
`W=2x+e^x` evaluated between `1 and 2` gives us:
`W=(4+e^2)-(2+e)=2+e^2-e=2+e(e-1)=6.67~~6.7J`