# Question #44212

Oct 10, 2017

Your teacher's statement is right - depending on the situation.

#### Explanation:

I am assuming that you are saying that the teacher said "work done is equal to kinetic energy". Both work and kinetic energy are in units of Joules. The teacher's statement is an example of the principle of conservation of energy.

Energy is required to do work. Consider a situation in which you are pushing something to give it kinetic energy. You are doing work. The source of the energy you need to do this work would be calories in the diet you have eaten. When you have given the object some kinetic energy, that object now possesses that energy.

It is necessary to properly interpret that statement "work done is equal to kinetic energy". It depends on the situation. Work can also be be done in a way that the energy is turned into heat, or electrical energy or several other forms. So there are situations in which that statement would not be true.

The teacher's statement would be true, if the situation you have been considering is one where work is being done to accelerate an object. The work done (measured in Joules) accelerating the object will be the kinetic energy gained (measured in Joules). But there are still conditions to consider.

In learning Physics we often choose to ignore friction. This choice greatly simplifies the problem. But you might say that it is an improper assumption. We live in the real world and the real world has friction. If we consider friction, some of the Joules of work you do convert to the kinetic energy form and some of the Joules are in the chore of dealing with friction. These Joules end up as heat.

So I expect that the situation when your teacher said that had details that you did not describe for us.

I hope this helps,
Steve

Oct 11, 2017

see below

#### Explanation:

the definition of kinetic energy is

the work done/required in bringing an object to rest.

This will mean that if an object is accelerated from one velocity to another then the the change in kinetic energy is the work done in change the state of the object

say the initial velocity $= u$

final velocity $= v$

mass$= m$

accelaration$= a$

distance moved $= s$

force applied$= F$

then

Work Done from initial to final state

$W D = F s$

by N2L$\text{ } F = m a$

$W D = m a s - - \left(1\right)$

but by constant acceleration eqns

${v}^{2} = {u}^{2} + 2 a s$

$\therefore a s = \frac{1}{2} \left({v}^{2} - {u}^{2}\right) - - \left(2\right)$

$\left(2\right) \rightarrow \left(1\right)$

$W D = \frac{m}{2} \left({v}^{2} - {u}^{2}\right)$

$W D = \frac{1}{2} m {v}^{2} - \frac{1}{2} m {u}^{2} = \text{ the change in KE}$