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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 \times 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.

$ \Rightarrow W = \Delta K $

Putting the value of work from above, we have

$ \Rightarrow \Delta K = F \times s $

We know that

$ F = ma $

$ \Rightarrow \Delta K = ma \times s $

We also know that

$ {v^2} - {u^2} = 2as $

Since $ u = 0 $

We have , $ s = \dfrac{{{v^2}}}{{2a}} $

Putting the value of s in above equation, we have

$ \Delta K = ma \times \dfrac{{{v^2}}}{{2a}} $

$ \Rightarrow \Delta K = \dfrac{1}{2}m{v^2} $

Hence the net work done to change is kinetic energy.

$ \Rightarrow \Delta K = $ Final Kinetic energy – Initial Kinetic Energy

Since finally , the object is coming to rest,

So Final Kinetic Energy = $ 0 $

$ \Rightarrow \Delta K = $ $ 0 $ – Initial Kinetic Energy

$ \Rightarrow \Delta K = - \dfrac{1}{2}m{v^2} $

Hence the work done on the object is $ - \dfrac{1}{2}m{v^2} $ .

Since the net work done is coming negative in this case , so a total amount of work = $ \dfrac{1}{2}m{v^2} $ is required to be done on the object , in order to bring the object to rest . So negative work means that work needs to be done on the object.