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Beginning Math and Physics for Game Programmers by Wendy Stahler

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Chapter 10, “Motion in Two and Three Dimensions”

2D Displacement

Δr = rfri

for position vectors ri (initial) and rf (final).

Average Velocity in 2D and 3D

for any displacement vector Δr and time interval t.

Equations of Motion in 2D and 3D

vf = vi + at

Δx = ½(vf + vi)t

Δx = vit + ½at2

for vectors a, vf, vi, and Δx and scalar t.

Vertical Components of a Projectile

ay = –9.8m/s2

vfy = viy + at

Δy = viyt + ½ayt2

Horizontal Components of a Projectile

ax = 0m/s2

vx = Δx/t

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