# An object has a mass of #6# #kg#. The object's kinetic energy uniformly changes from #42# #kJ# to # 15# #kJ# over #t in [0, 6 s]#. What is the average speed of the object?

##### 1 Answer

Find the average kinetic energy and convert it to a speed, given the mass. The average speed is

#### Explanation:

Let me outline how I approached this problem, including what turned out to be a dead end.

Kinetic energy is given by:

Rearranging this to make

Using this, the initial velocity of the object is

If the speed change uniformly we could simply add these two speeds and divide by 2 to find the average, but the tricky bit here is that the question says the **kinetic energy** changes uniformly... and kinetic energy is proportional to the square of the speed.

Given that, we need to approach the problem from a different direction. The average kinetic energy will be given by:

Using the formula above for the speed gives: