  The classic brachistrochrone problem is standard material in intermediate
mechanics. Many variations exist including some accessible to introductory
students. While a quantitative solution isn't feasible in introductory classes,
qualitative discussions can be very beneficial since kinematics, Newton's Laws,
energy conservation and motion along curved trajectories all play a role. In
this work, we describe an activity focusing on a qualitative understanding of
the brachistochrone and examine the performance of freshmen, juniors and
graduate students. The activity can be downloaded at
https://w3.physics.arizona.edu/undergrad/teaching-resources .
