Question

The force applied against an object moving horizontally on a linear path is described by `F(x)=xe^x+ 1/x`. By how much does the object's kinetic energy change as the object moves from `x in [ 1, 3 ]`?

Answer 1

Approximately: `41.270 J`

Explanation:

The work done will be the integral of the force over the distance.
`W = int_1^3 F(x) dx= int_1^3 (xe^x+ 1/x) dx`
We'll leave the process of solving this integral to the student. The answer is:
`W = 2*e^3 + log(3) = 41.270 J`
Since we know that the work done is equal to the change in kinetic energy, we can say that:
`Delta KE = W = 41.270 J`