Question

The force applied against an object moving horizontally on a linear path is described by `F(x)=2x +4`. By how much does the object's kinetic energy change as the object moves from `x in [ 3, 5 ]`?

Answer 1

`Delta E_k=-16 J`

Explanation:

`W:" work doing"`
`E_k:" changing of the kinetic energy"`
`W=Delta E_k=int_a^b F(x) d x`
`W=Delta E_k=int _3^5(2x+4)*d x`
`Delta E_k=[2*1/2*x^2+4*x]_3^5`
`Delta E_k=[x^2+4x]_3^5`
`Delta E_k=(5^2+4*5)-(3^2+4*3)`
`Delta E_k=5-21`
`Delta E_k=-16 J`