Question

An object has a mass of `6 kg`. The object's kinetic energy uniformly changes from `18 KJ` to `4KJ` over `t in [0,12s]`. What is the average speed of the object?

Answer 1

9.47 m/s

Explanation:

Based on the given values, the power loss (which is the constant here) is
`P = (\Delta E)/t = (18\ KJ - 4\ KJ)/(12\ s) = -7/6 \ kW`
so `E = E_0 + Pt`.

We can then find the velocity at any time based on that equation:
`E = 1/2 mv^2 -> v(t) = sqrt(2E/m) = sqrt((2E_0)/m + (2P)/mt)`
From that equation, we can find its average:
`v_(ave) = 1/(12\ s) cdot int_0^(12s) v(t)dt = (2 (2E_0/m + (2P/m) cdot (12\ s))^(3/2))/(3 cdot 2P / m)`
`v_(ave)= (mv_f^3)/(3P) = 9.47\ m/s`

I hope the calculus is comfortable to you.