Beginning Math and Physics for Game Programmers

Chapter 12, "Energy"

Work

W = F D x

where D x = displacement and F = force in the direction of displacement.

Kinetic Energy

KE = ½ mv ²

where m = mass and v = speed.

Work-Energy Theorem

W = D KE = KE _f “ KE _i

or

where the force and displacement are in the same direction and v is speed.

Gravitational Potential Energy

GPE = mgy

where m = mass, g = acceleration due to gravity, and y = height.

Conservation of Mechanical Energy (Simplified)

KE _i + PE _i = KE _f + PE _f

or

Conservation of Mechanical Energy (Modified)

KE _i + PE _i = KE _f + PE _f + E _o

or

where E _o represents other energy (heat/sound).