Editing Racetrack (game) (section)

==Mathematics and physics==
Each move may be represented by a [[vector (geometry)|vector]]. E.g., a move four squares to the right and two up may be represented by the vector (4,2).

The eight neighbour rule allows changing each [[coordinate]] of the vector by ±1. E.g., if the previous move was (4,2), the next one may be any of the following nine:
::(3,3) (4,3) (5,3)
::(3,2) '''''(4,2)''''' (5,2)
::(3,1) (4,1) (5,1)

If each round represents 1 second and each square represents 1 metre, the vector representing each move is a [[velocity|velocity vector]] in metres per second. The four neighbour rule allows [[acceleration]]s up to 1 metre per second squared, and the eight neighbours rule allows accelerations up to {{radic|2}} metres per second squared.  A more realistic maximum acceleration for car racing would be 10 metres per second squared, e.g. corresponding to assuming each round to represent a [[reaction time]] of 0.5 seconds, and each square to represent 2.5 metres (using 4 neighbour rule).

The speed built up by acceleration can only be reduced at the same rate. This restriction reflects the [[inertia]] or [[momentum]] of the car. Note that in physics, speeding, braking, and turning right or left all are forms of acceleration, represented by one vector. For a sports car, having the same maximum acceleration without loss of traction in all directions is not unrealistic; see [[Circle of forces]]. Note, however, that the [[circle of forces]] strictly applies to an individual tyre rather than an entire vehicle, that a slightly elongated ellipse would be more realistic than a circle, and that the theory of traction involving this circle or ellipse is quite simplified.