How can we deduce the units of energy from the definition of kineticenergy?

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How can we deduce the units of energy from the definition of kinetic
energy?

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Step 1

The kinetic energy is the energy required to move any mass m with velocity v. In other word work required to move any body.

In mathematically, it is half of product of mass and square of  velocity. That is,

K.E=12mv2

Using equation of motion,

v2=u2-2as

Since body start from rest, so

v2=2asa=v22s

So force required

F=ma=m×v22s=12mv2s

So work done, to move object

W=Fs=12mv2s×s=12mv2

So the kinetic energy is,

K.E=12mv2

So unit,

K.E=12mv2=kg×m/s2=kgm2s-2=J

 

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