Now find the gravitational potential energy U(z) of the object when it is at an arbitrary height z. Take zero potential to be at position z=0. Keep in mind that the potential energy is a scalar, not a vector. Express U(z) in terms of m, z, and g. c) In what direction does the object accelerate when released with initial velocity upward? d) Find F(z), the electric force on the charged particle at height z.

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.