Motion Graphs and Calculus

We know that velocity is change in displacement, and acceleration is change in velocity. Calculus tells us that the rate of change of a function is the derivative, and therefore we can differentiate and integrate to convert between different functions of displacement, velocity and acceleration.

graph LR
	A(Displacement) --->|Differentiation| B(Velocity) --->|Differentiation| C(Acceleration)
	C --->|Integration| B --->|Integration| A


v=dsdt      a=dvdtv=a dt      s=v dt
Variable Key

  • s is displacement.
  • v is velocity.
  • a is acceleration.
  • t is time.