That's just not right. If I'm traveling at a steady 100 kph and hit the brakes, my acceleration is negative. Acceleration is just the rate of change of velocity--the slope of line describing how my velocity changes over time. If I'm stopped, shift into reverse, and hit the gas then my acceleration is still positive because my velocity is increasing (just in the "negative direction" relative to where I started). If my velocity is increasing, my acceleration is positive. If my velocity is decreasing, my acceleration is negative. It doesn't matter what direction I'm going.
That's just not right. If I'm traveling at a steady 100 kph and hit the brakes, my acceleration is negative. Acceleration is just the rate of change of velocity--the slope of line describing how my velocity changes over time. If I'm stopped, shift into reverse, and hit the gas then my acceleration is still positive because my velocity is increasing (just in the "negative direction" relative to where I started). If my velocity is increasing, my acceleration is positive. If my velocity is decreasing, my acceleration is negative. It doesn't matter what direction I'm going.
You're correct, the rate of change of speed is velocity and not acceleration.
Velocity is the rate of change of position.