A thin, hollow sphere (with moment of inertia ) rolls without slipping down an inclined plane. The sphere starts from rest at the top of the incline. The following are true about the sphere-inclined plane system: Find the translational speed of the sphere at the bottom of the incline. What Big Idea is the most appropriate one for solving this problem

You get 6 for mechanical

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.