An object has a mass of 6 kg. The object's kinetic energy uniformly changes from 84 KJ to 12 KJ over t in [0, 6 s]. What is the average speed of the object?

1 Answer
reudhreghs
Feb 27, 2017

115.3ms^-1

Explanation:

E_k = 1/2mv^2

This is the equation for kinetic energy. It can be rearranged to give v as the subject:

v = sqrt((2E_k)/m)

We know the mass m=6 and the energy at the beginning is E_k = 84kJ = 84000J, so

v = sqrt((2*84000)/6) = sqrt(28000) = 167.332ms^-1

We know that the energy at the end is 12kJ = 12000J, so

v = sqrt((2*12000)/6) = sqrt(4000) = 63.25ms^-1

Now we have the initial and the final velocities.

Work out the average (of anything) by adding them all together and dividing by the total number of things. In this case, we only have two velocities, so:

bar v = (167.332 + 63.25)/2

= 115.291ms^-1

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