Beginning Math and Physics for Game Programmers

Chapter 9, "Derivative Approach to Motion in One Dimension"

Average Velocity

equals the slope between two points on position v . Time graph for any time interval a t b .

Instantaneous Velocity

at t = a for any function f ( t ) that gives position as a function of time.

Instantaneous Velocity

v = f '( t )

for any position equation that's a function of time, f ( t ).

Average Acceleration

equals the slope between two points on velocity v . Time graph for any time interval a t b .

Instantaneous Acceleration

for any function f ( t ) that gives velocity as a function of time.

Instantaneous Acceleration

a = v '( t )

for any velocity equation that's a function of time, v ( t ).

Instantaneous Acceleration

a = v '( t ) = y ''( t )

for any velocity equation that's a function of time, v ( t ), and any position equation that's a function of time, y ( t ).