distinguish between theoretical mechanical advantage and actual mechanical advantage. How would these compare if a machine were 100% efficient?

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. 

Planck decided to assume that atoms could only vibrate at certain frequencies that were whole numbers eg 2f, 3f and so on. others used to think that atoms vibrate continuously

What is on your multiple choice anwers