Show how the equation for KE has units of joules.

The SI unit of kinetic energy is Joules.

Explanation:

The unit of work done is Joules.

Work done = Force × displacement

For units :

W = N×m

N is newton (unit of force) and m is metre

N = kg m/s²

⇒ W = kg m/s² × m

W = kgm²/s² (1)

Kinetic energy of an object is given by :

K = (1/2) mv²

For units :

K = kg× (m/s)²

K = kgm²/s² (2)

We know that, kgm²/s² = Joules

From equation (1) and (2), we find that both work done and kinetic energy have same unit i.e. Joules.

yes it is balanced