# An object has a mass of #4 kg#. The object's kinetic energy uniformly changes from #144 KJ# to # 124KJ# over #t in [0, 6 s]#. What is the average speed of the object?

##### 4 Answers

I found:

#### Explanation:

From your Kinetic Energies you can work out the speed (at two instants of time) knowing that kinetic energy

so, rearranging:

Now we use the kinematic relationship:

to get:

and:

and the other relationship:

The average speed during your time interval will then be:

**ALTERNATIVE**

If Eq(2) is divided by Eq (1) we get

**av velocity**

If Initial velocity be u m/s and final velocity v m/s after 6 s

then

Again

average speed for uniform change in velocity( i.e. having uniform retardation) =

**If uniform change in KE with time is considered then calculation will not match with this one**

From the graph

#### Explanation:

It is given that the Kinetic energy changes uniformly.

We know that

Divide the given change in velocity by

Calculate velocities at time

Observe that the change in velocity in each second interval is not constant. As such, acceleration is not constant. Therefore, the known expressions for linear motion for constant acceleration can not be applied.

I have attempted to assess Approx Average velocity by calculating distance moved in each second. This is approximately equal to the velocity for that second. Take the sum of these six distances and divide by time that is

More accurately, one should draw a

Area Graph added

~~258.8m/s#

#### Explanation:

Initial KE

After 6s Final KE

KE is uniformly decreased, so it will have a constant negative slope

and this slope will be

If at t th instant

**We are to find out a relation between v and t**

the KE at t th instant

Now

Now distance traversed during 6 s

Let

when

when

Hence the average speed