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In this section we encounter the first of many 'mathematical asides' in the book (always indicated by a grey background). The amount of mathematics needed at this level is neither particularly extensive nor especially demanding. Most learners find mathematical concepts easier to grasp if the ideas are introduced within a relevant physical context. 

The concept of velocity in one dimension is a good example of a derivative. A brief formal introduction to differentiation is provided but it is important that you assimilate what you learn here with any similar material you have already studied in a course in mathematics. It may help understanding to view the simple  applet . 

The derivative of velocity with respect to time is the acceleration, a quantity that turns out to play a very important role in dynamics.

A good interactive exercise on constant acceleration in one-dimension is provided on the Student Companion Site of Halliday, Resnick and Walker: Principles of Physics, 9th Edition. Click here on  and play with different values of initial position (x0), initial velocity (v0) and acceleration (a).  Initially try the following values      (a) x0 = 0 m;  v0 = 0 m/s;  a = 0.5 m/s2      (b) x0 = 0 m;  v0 = – 3.0 m/s;  a = 0.5 m/s2      (c) x0 = 0 m;  v0 = 5.0 m/s;  a = – 1.0 m/s2  and continue to use the simulation interactively until you have mastered the concepts involved.

You may also find it helpful to return to the  from the  website to complete the remaining simulations  and  and study the