An object has a mass of 6 kg. The object's kinetic energy uniformly changes from 88 kJ to 48 kJ over t in [0, 6 s]. What is the average speed of the object?

1 Answer
David G.
Mar 23, 2016

From the kinetic energy and the mass given, the initial speed is 5.4 ms^-1 and the final speed is 4 ms^-1. The average speed is 4.7 ms^-1.

Explanation:

I don't think we actually need to know the time taken. Let's find out.

We know E_k=1/2mv^2, which we can rearrange to give:

v=sqrt(2E_k/m)

That means the initial speed (we don't care about direction) is:

v=sqrt(2E_k/m)=sqrt(2xx(88)/6)~~5.4 ms^-1

The final speed is:

v=sqrt(2E_k/m)=sqrt(2xx(48)/6)=4 ms^-1

Since the object is decelerating uniformly, the average speed will just be:

(v_"initial"+v_"final")/2 = (5.4+4)/2 = 4.7 ms^-1

Whether it decelerated over 1, 2 or 6 seconds, the average speed would be the same.

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