Question

The force applied against a moving object travelling on a linear path is given by `F(x)= x^2+4x`. How much work would it take to move the object over `x in [0, 4]`?

Answer 1

I found: `53.bar(3)J`

Explanation:

Here I would use the integral definition of work for a variable force as:
`W=int_(x_1)^(x_2)F(x)dx=int_0^4(x^2+4x)dx=`
`=x^3/3+cancel(4)^2x^2/cancel(2)=` evaluated between `0` and `4`:
`=(4^3/3+2*4^2)-0=160/3J=53.bar(3)J`