Game Development Reference
In-Depth Information
Velocity
Start
Acceleration
Velocity
Reversing Direction
Acceleration
Velocity
Moving In Opposite Direction
Acceleration
Figure 5-1.
Car reversing then moving backward
Figure
5-1
shows the velocity and acceleration vectors for this car as it moves down the street,
slows down, and then reverses direction.
Average velocity is the change in distance divided by the change in time. Figure
5-2
shows this
definition, with the variable x representing the position and t representing time.
Figure 5-2.
Average velocity definition
The average velocity may be a good representation, if the car maintains a constant speed
throughout the time interval. However, if during the time interval the car's speed is extremely high
during one portion and extremely low during another, the average speed would not be a good
representation of the car's behavior.
The instantaneous velocity is the change in position of an object divided by the change in time when
the time interval approaches 0. If you are given a function that represents the position of an object
with respect to time x(t), then the first derivative of that function, or x'(t), is the velocity function.
(See Figure
5-3
.)
