Question

Which gives the correct relationship for kinetic energy?1) KE = mv2) KE = mv23) KE = mv/24) KE = mv2/2

Answer 1

4) KE = mv²/2

Step-by-step explanation

Kinetic energy is the energy of an object because of its motion. If we want to move an object we have to apply a force, which means that we have to do work. After work is done, energy is transferred to the object. This is kinetic energy.

If we want to find this energy we can start by finding the work W done by a force F when we want to move the object a distance d:

`W=F\cdot d`

And to move the object the force must be:

`F=m\cdot a`

So the work is:

`W=m\cdot a\cdot d`

Using the kinematic formula:

`v^2=v^2_0+2ad`

That we can solve for a:

`a=(v^2-v^2_0)/(2d)`

Now, replacing a by this expression in the work formula above:

`W=m\cdot d\cdot(v^2_f-v^2_i)/(2d)=m\cdot(v^2_f-v^2_i)/(2)=(1)/(2)mv^2_f-(1)/(2)mv^2_i`

This work is equivalent to the change of kinetic energy of the object. This means that for any speed v, the kinetic energy is:

`KE=(1)/(2)mv^2`

So the correct answer is option 4