“The rate of change of a function” is the definition of a derivative. You might as well ask “Why does the circumference of a circle equal the length of the edge of the circle?”

For a curve like a position equation, the slope at any given point is equal to how fast the position is changing. The speed of a change in position is called “velocity.”

When graphing your change in displacement with respect to time there is a slope for that line. The slope is the rate of change in that line. This slope is velocity.

Velocity describes the direction and change of displacement with respect to time.

So think of this: you move forward for some amount of time. Do you move forward with a constant speed? Do you run for a while? Do you stop to tie your shoe for a moment? Did you forget your phone at home and have to go back? This change is the velocity. If you were to graph this change in displacement with respect to time, the slope of the line would be your velocity.

Since derivatives are the rate of change of a function with respect to an independent variable, velocity is the derivative of displacement with respect to time.

I hope this makes sense and doesn’t sound too repetitive.

## Latest Answers