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What is the rate of change in position or rate of motion?
Velocity, which is different than speed in that it has a directional component to it.
Is the motion down slope occurring at a constant or change rate?
changing. only under specific requirements would the motion be constant.
What is rate of change of speed?
We look at acceleration as the rate of change of speed.Technically rate of change of velocity is acceleration. However speed and velocity are interchangeably used while problem solving, the vector property of motion is considered deliberately rather than as a rule.In other words acceleration can be also called rate of change of speed....Sounds daaah.....that's why humanity is yet to make great leap in science...we are to understand light, gravity, etc....we are scared of precise definitions.
What is the geometrical meaning of second derivative?
The first derivative is the rate of change, and the second derivative is the rate of change of the rate of change.
How is the steepness of the line is related to the rate of change?
the steepness of the line is the slope of the line which is the rate of change; the steeper the slope, the faster the rate of change
