What happens to the speed of different colors of light when they enter a glass prism?

Light slows down when it enters glass. The amount depends on the colour: glass has a higher refractive index for violet light than for red light.

Since n = speed in air ÷ speed in glass, a higher n means a lower speed in glass. So violet light slows down more than red light.

That is why violet bends the most and red the least, and a prism splits white light into a spectrum.