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
Mar 23, 2016

Answer:

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.