I ran into a rather abstruse question in today's first mechanics recitation. The question gave the one dimensional position of a particle with respect to time as
$x = 10 - 4t + 2t^3$
It then asked for the distance traveled by the particle between t = 0 and t = 2. The suggested answer, (from the prof in charge of TAs), was to plot the trajectory of the particle, thereby demonstrating the distance and displacement were different. Here's the plot:
Plot the position vs. time
Show the graph of dx/dt vs. time with all distance positive
More to come...