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
Feb 12, 2018

Answer:

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.