A student is attempting to determine the coefficient of static friction between a coin and a steel plate. The student attaches the center of the plate to a freely rotating axis. For each trial, the student sets the coin on different positions on the steel plate and measures the distance from the center of the coin to the center of the axis of rotation. The student also has a stopwatch to measure the period T of the plate's rotation Required:
Explain how the student can use this setup to take measurements that would allow the coefficient of static friction to be calculated.

The best description is: . nobody has any idea what q is.

You need to be more specific.  i really don't know what a "motion map" is.you can draw a graph of an object's position, distance, displacement, speed,velocity, or acceleration versus time, or you can draw a graph of the object's x-position versus its y-position and not give any information about time at all.if the graph presents position or displacement against time,  then constant velocity is a straight line . . i.e. a line that has  constant slope.if the graph shows speed against time, then constant velocityis a horizontal piece of line.if the graph shows acceleration against time, then constant  velocity is a piece of line that lies on the x-axis . . it's value is zero.