# An object has a mass of #4 kg#. The object's kinetic energy uniformly changes from #640 KJ# to # 160 KJ# over #t in [0, 12 s]#. What is the average speed of the object?

##### 3 Answers

The average speed is

#### Explanation:

The kinetic energy is

mass is

The initial velocity is

The final velocity is

Therefore,

and,

The graph of

The points are

The equation of the line is

So,

We need to calculate the average value of

So,

average speed is defined as total distance travelled divided by total time taken to cover that distance .

#### Explanation:

the kinetic energy of a body of mass m moving with speed v is defined as :

thus you can calculate velocity of body at the starting and the end of interval of time :

lets say initially the velocity was

let at the end of interval of time the velocity was

now , total distance travelled by the body over given time interval can be calculated by using

thus,

average speed is defined as ratio of total distance travelled and total time taken :

Let rate of change of kinetic energy be

where

Integrating both sides with

where

To evaluate

We have expression for kinetic energy as

To evaluate

Equation (1) becomes

If

Given is

Average speed