Question

An object has a mass of `6 kg`. The object's kinetic energy uniformly changes from `120 KJ` to `36 KJ` over `t in [0, 4 s]`. What is the average speed of the object?

Answer 1

`bar v =159.178`

Explanation:

Calling `t_1=0, t_2= 4,E_1=120000,E_2=36000,m=6`
interpolating the kinetic energy `e` we get
`e = E_1+((E_2-E_1)/(t_2-t_1))(t-t_1)` but `e = 1/2mv^2`
also
`v = sqrt(2e/m)`. Average speed is obtained calculating
`bar v =( int_{t_1}^{t_2}v dt)/(t_2-t_1) = 159.178`