Question

an object of mass m moving with constant velocity v has kinetic energy (1/2)mv².what is the work done to stop this object

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Answer 1

Answer:

According to Work Energy theorem , The net work done on an object is equal to the change in its Kinetic Energy. Hence the net work done to change is kinetic energy. Hence the work done on the object is $ - \dfrac{1}{2}m{v^2} $

Explanation:

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Answer 2

We know that every object possesses some energy whenever it is moving.

That energy is termed as Kinetic Energy.

Also since the car is moving , it is doing some work.

Work=It is the measure of energy transfer which occurs when a force is applied on an object causing it to move to some distance.

W=F×s

Where W= work done

F= Force applied

s=displacement

According to law of conservation of energy can neither be created nor be destroyed. It can be transferred from one form to another.

So work done by the car is changed to its kinetic energy.

According to Work Energy theorem ,

The net work done on an object is equal to the change in its Kinetic Energy.

⇒W=ΔK

Putting the value of work from above, we have

⇒ΔK=F×s

We know that

F=ma

⇒ΔK=ma×s

We also know that

v2−u2=2as

Since u=0

We have , s=v22a

Putting the value of s in above equation, we have

ΔK=ma×v22a

⇒ΔK=1/2mv2

Hence the net work done to change is kinetic energy.

⇒ΔK= Final Kinetic energy – Initial Kinetic Energy

Since finally , the object is coming to rest,

So Final Kinetic Energy = 0

⇒ΔK= 0 – Initial Kinetic Energy

⇒ΔK=−1/2mv2

Hence the work done on the object is −12mv2

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