Game Development Reference

In-Depth Information

Whether you are looking at problems involving particles or rigid bodies, there are some

important kinematic properties common to both. These are, of course, the object's po‐

sition, velocity, and acceleration. The next section discusses these properties in detail.

Velocity and Acceleration

In general, velocity is a vector quantity that has magnitude and direction. The magnitude

of velocity is speed. Speed is a familiar term—it's how fast your speedometer says you're

going when driving your car down the highway. Formally, speed is the rate of travel, or

the ratio of distance traveled to the time it took to travel that distance. In math terms,

you can write:

v = Δs/Δt

where
v
is speed, the magnitude of velocity
v
, and Δ
s
is distance traveled over the time

interval Δ
t
. Note that this relation reveals that the units for speed are composed of the

basic dimension's length divided by time,
L/T
. Some common units for speed are meters

per second,
m/s
; feet per second,
ft/sec
; and miles per hour,
mi/hr
.

Here's a simple example (illustrated in
Figure 2-1
): a car is driving down a straight road

and passes marker one at time
t
1
and marker two at time
t
2
, where
t
1
equals 0 seconds

and
t
2
equals 1.136 seconds. The distance between these two markers,
s
, is 30 m. Calculate

the speed of the car.

Figure 2-1. Example car speed

You are given that
s
equals 30 m; therefore, Δ
s
equals 30 m and Δ
t
equals
t
2
− t
1
or 1.136

seconds. The speed of the car over this distance is:

v = Δs/Δt = 30 m/1.136 sec = 26.4 m/sec

which is approximately 60 mi/hr. This is a simple one-dimensional example, but it brings

up an important point, which is that the speed just calculated is the average speed of the

car over that distance. You don't know anything at this point about the car's acceleration,