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?

1 Answer
Jake M.
Feb 12, 2018

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.

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