# 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

$$\mathrm{[N]=[kg\cdot m/s^2]}$$
which you can convince yourself of from Newton's second law $F=ma$. Plug it into $\mathrm{[N\cdot m]}$ and you'll see.