Question

Why do you keep moving forward when you slam on the brakes of your bike?

Answer 1

Because the act of braking is an example of negative acceleration.
Example: if the rate of braking was say 2 meters per second^2, and the starting velocity was 10 m/s, it would take 5 seconds to come to a stop(during those 5 seconds you would still be moving).

Answer 2

If you're going really really slow and you hit the brakes, you're going to stop almost instantly. When you're going faster, you've got your energy which is your body size so it takes energy to stop the bike. When you slam the brake you're trying to apply that energy to the wheels. Even if you lock them up so the wheels aren't spinning, you skid because friction is rubbing against the ground and that will be what eventually stops you.

If you have a wider tire, you're going to have more surface area hitting the ground and that will cause more friction so you will stop faster. If you have skinnier tires you will skid more so there are a bunch of different factors.