Yes in a form. It can not be literaly -20mph but in deceleration it is. when you slow down a car to a stop that is negative volocity. and volacity is speed+direction. ex: 30mph east. so if your travaling 20mph west then slow to a stop it changes to -20mph west. (until you start going east) but because volacity is a messure of speed then yes it is possible. but not like when approching the speed of light when time slows down, if you go slower than it by so much then it speeds up. (because the speed cant be that form and has to be in directiog)
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The problem here is the conflating of the term "speed" with "velocity".
Velocity is a vector - it has both intensity and direction. Velocity can be negative.
Speed really only has magnitude, so it is normally only positive; since there is no direction associated you can't define a meaning for negative speed (unless you decide to define it as synonymous with velocity)
When a body is thrown in upward direction and upward motion is defined as positive velocity, its velocity decreases with time and at highest point speed and velocity become zero. When the body falls downward its speed i increases until hit the ground but since it is moving in the opposite of the direction that was defined as "positive", its velocity is negative.