What is the word for an increase in speed (not velocity)?

the best thing i could think of would be acceleration.

Going faster? Faster would be a term for an increase in speed.

Its acceleration, nothing else.
Acceleration doesn't show direction, for that we have negative acceleration/retardation.

to go FASTER would mean to increase the rate at which something is moving thus equaling increased speed

Well, using calculus as a guide the answer does point to acceleration as well
Hopefully, you can follow along with this explanation:
The derivative of velocity gives acceleration, dv/dt = acceleration, and looking at the units for acceleration it's d/t² (distance over time squared) (For example m/s²)

Velocity does have the same units as speed, (For example m/s) so, with that being said, if you take the derivative of speed you should expect to find acceleration

This makes sense because velocity really is just a more definitive form of speed, it represents the same number only difference is speed can't be negative.

Acceleration is ambiguous.  Its actually very complicated.  Acceleration is the most complicated phoenomenon there is.  Honestly is is the only word to describe what you are looking for but in realistic terms, slowing down is a vector.  Think of it this way.  Your car must exert a force to slow you down.  The force is applied which is a vector, and that force causes a deceleration.  Honestly there is no word because it would be redundant however you look at it.