Question

The force applied against an object moving horizontally on a linear path is described by `F(x)= cospix+1`. By how much does the object's kinetic energy change as the object moves from `x in [ 2, 5 ]`?

Answer 1

`Delta E_k=3J`

Explanation:

`"Work done by Force is equal to changing kinetic energy in interval(2,5)"`
`Delta E_k=W=int _2^5 (cos pi x+1)d x`
`Delta E_k= int_2^5(cos pi x)d x+int_2^5d x`
`Delta E_k=[-1/pi sin pix]_2^5+[x]_2^5`
`Delta E_k=[-1/pi sin 5 pi-(-1/pi sin 2 pi)]+(5-2)`
`Delta E_k=[-1/pi 0-(-1/pi 0)]+3`
`Delta E_k=3J`