Using Derivatives: Redefining velocity and acceleration using motion graphs

 Calculus is one of the greatest discoveries in STEM history, and I would say in human history. Isaac Newton developed it in his studies of motion and gravity, and it is a 'tool' we will use from here on out once we get some understanding of derivatives (and later 'anti-derivatives', which will allow us to use integrals). 

Motion graphs like position vs time, velocity vs time, and acceleration vs time, are common features used to analyze motions of objects. And from last year, you may have even related velocity and acceleration to slopes of other graphs. But remember, derivative just means slope, too, only of tangent lines. 

We will now define v = dx/dt, and a = dv/dt...using slopes of tangent lines of strange curves, to determine the motion of object. This takes us to ANY MOTION, not just constant acceleration like last year!! 

Check this out to start getting some understanding.