Game Development Reference
In-Depth Information
Figure 11.9
Plots of position, velocity, and acceleration over time.
•
A discontinuity in the velocity function causes a “kink” in the posi-
tion graph. Furthermore, it causes the acceleration to become infinite
(actually, undefined), which is why, as we said previously, such dis-
continuities don't happen in the real world. This is why the lines in
the velocity graph are connected at those discontinuities, because the
graph is of a physical situation being approximated by a mathematical
model.
•
A discontinuity in the acceleration graph causes a kink in the velocity
graph, but notice that the position graph is still smooth. In fact,
acceleration can change instantaneously, and for this reason we have
chosen not to bridge the discontinuities in the acceleration graph.
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