How can Work and Kinetic Energy have the same units?

If work is Force x Displacement, it would result to N x m, which is Joules. But then, kinetic energy is 0.5mv^2, which is kg x m^2/s^2. Can anybody tell me a way to prove that they have the same units?

Edit: I just found a way, but I am not sure if it is valid.

Weight is a force, and it is computed by: mass x acceleration, which is kg x m/s^2 (or Newtons) So, if KE is kg x m^2/s^2, then it becomes N x m

2 Answers

The Newton unit is not a fundamental unit but consists of:

$$\mathrm{[N]=[kg\cdot m/s^2]}$$

which you can convince yourself of from Newton's second law $F=ma$. Plug it into $\mathrm{[N\cdot m]}$ and you'll see.

Work and kinetic energy are interchangeable, so they are the same, ie. they have the same units. Your work can give kinetic energy to a body and a body with kinetic energy can produce work.

• Work and kinetic energy are not interchangeable. They are fundamentally different kinds of quantities, although they are related and have the same units. The net work done on a point particle is equal to the change in kinetic energy of the particle. Work is then a transfer of energy to or from the particle due to forces that act on the particle, and the net result of these forces is to (possibly) change the kinetic energy of the particle. In any case, this doesn't really answer the question. – march Nov 16 '15 at 2:52