In a speed vs. time graph where a curve is depicted, why does the slope of a tangent line drawn to the curve represent the instantaneous speed, and not the average speed?
1 Answer
Apr 10, 2015
It represents neither, as-written.
The average velocity (or speed , the magnitude of velocity) is the velocity across an entire interval of time for a change in position. The instantaneous velocity is according to one miniscule moment in time, such as 1 femtosecond in the context of several seconds.
Imagine zooming into a position vs. time graph so much that it looks linear. That's the derivative for a position vs. time graph (velocity in some direction). The slope of the tangent line for a velocity vs. time graph is the instantaneous acceleration, not the velocity. Since this slope can be positive or negative, I said velocity rather than speed.
