Beginning Math and Physics for Game Programmers

Chapter 10, "Motion in Two and Three Dimensions"

2D Displacement

D r = r _f “ r _i

for position vectors r _i (initial) and r _f (final).

Average Velocity in 2D and 3D

for any displacement vector D r and time interval t .

Equations of Motion in 2D and 3D

v _f = v _i + at

D x = ½( v _f + v _i ) t

D x = v _i t + ½ at ²

for vectors a, v _f , v _i , and D x and scalar t .

Vertical Components of a Projectile

a _y = “9.8m/s ²

v _fy = v _iy + at

D y = v _iy t + ½ a _y t ²

Horizontal Components of a Projectile

a _x = 0m/s ²

v _x = D x / t