Yes
velocity is a vector that has both speed and direction. So if you are going 30 mph in one direction that may be positive, but if you are going in reverse that may be negative.
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It cannot have negative velocity, it can have negative acceleration.
An absolute value can never be a negative. An absolute value is just the distance the # is from the zero...so again for it to be negative thats not possible
Positive X or Negative X
Velocity is a vector, which means it has a direction, but speed isn't. Speed is the absolute value of velocity. Velocity can be negative, meaning that the speed is opposite to the direction that you're calling the positive direction.
No, Speed is always greater than or equal to zero. However, velocity can be negative, which just means you have a positive speed in the opposite direction! (scalar(number) versus vector).