Motion graphs and derivatives

The derivative of a position vs. time graph is a velocity. Let’s say that position is measured in meters and time is measured in seconds. Now lets put position on the y axis and time on the x axis. The slope of a line is change in y over change in X. The Y values are position measured in meters and the x values are time measured in seconds. So y over x is meters per second. Velocity is measure in meters per sec. So the slope or derivative of a position vs. time graph is velocity.

This fact holds true for velocity vs. time graph. The derivative of a velocity vs. time graph is a acceleration. Again let’s use MKS. (Velocity in m/s and time in s) This time let’s put velocity on the y axis and time on the x axis. And again the slope of a line is change in y over change in X. The Y values are velocity measured in m/s and the x values are time measured in sec. So y over x is meters per second per second. Acceleration is measured in meters per second per second. So the slope or derivative of a velocity vs. time graph is accleration.

Another interesting fact about a velocity vs. time graph is the area under the line is the distance traveled. Velocity is on the y axis and time on the x access. Multiply the velocity times the time. The seconds cancel and you’re left with just meters. m/s X s = m.

The same multiplication rule holds true for acceleration vs. time graphs. When you multiply acceleration (m/s/s) by time (sec) you get velocity (m/s). m/s/s X s = m/s.