We got a long way with this equation, which came from one of the constant acceleration equations in the y-direction.
½m vy2 = ½m voy2 + may Dy
We can do the same thing in the x-direction, to get:
½m vx2 = ½m vox2 + max Dx
Are we adding vectors or scalars here?
Another thing we can do is to add the equations. This gives:
½m vx2 + ½m vy2 = ½m vox2 + ½m voy2 + max Dx + may Dy
Let's simplify this a bit:
½m v2 = ½m vo2 + max Dx + may Dy
Now, max is the x-component of the net force, and may is the y-component of the net force, so:
½m v2 = ½m vo2 + FNETx Dx + FNETy Dy
Is there some way to simplify this? We also need to keep in mind when a term like FNETx Dx is positive and when it is negative.
The equation can actually be written as:
½m v2 = ½m vo2 + FNET · Dr
What should we call this new quantity FNET · Dr? It is some kind of energy.
Let's call it the work done by the net force.
This work done is: