Physics Demonstrations

In this demonstration, we explore the relationship between the different differentiations of the position function. In physics, our base measurements are time, mass, and length. We combine length and time into a position function. In this demonstration, we use the position function of:

$f(x)=720{\mathrm{pop}}_{}{t}^6+120\times \mathrm{crackle}{t}^5+24{\mathrm{snap}}_{}{t}^4+6{\mathrm{jerk}}_{}{t}^3+2{\mathrm{acceleration}}_{}{t}^2+{\mathrm{velocity}}_{}t+{\mathrm{position}}_{}$

In this equation we have some unfamiliar terms. In order to find the motion with respect to time, we need to differentiate the equation with respect to time ($\mathrm{df}(x)/\mathrm{dt}$). We differentiate once, we have velocity. Differentiate twice, we have acceleration. Three times, jerk. Four times, snap. Five times, crackle. Six times, pop. The plot demonstrates the motion due to the different terms with respect to time.

Some questions to consider when viewing the demonstration:

• Analyze the affect each derivative has on the position, velocity, and acceleration functions.
• We understand the concepts of poistion, velocity, and acceleration; but what everyday concepts does jerk, snap, crackle, and pop represent?