Beginning Math and Physics for Game Programmers

Visualizing Acceleration and Second Derivative

The preceding section took a closer look at instantaneous velocity, and you ended up computing derivatives. This section goes one step further by delving deeper into the realm of acceleration, which leads to the concept of a second derivative. Let's start by taking a graphical approach again.

Rather than graph an object's position versus time, let's graph an object's speed or velocity versus time. Suppose a race car driver starts at a dead stop and floors the gas pedal. At regular intervals, his instantaneous velocity is recorded. These values are shown in Table 9.2.

Table 9.2. A Race Car's Velocity at Various Times

t (in sec)	v (in m/s)
0	0
1	3
2	12
3	27
4	48
5	75
6	108

You can graph these points to see how the ...