Obtain an expression for their relative speed of approach at any instant as a function of their separation distance d if the only interaction is their gravitational attraction to each other. Express your answer in terms of some or all of the variables m, d, and gravitational constant G. g

Pe = 1/2k(x)^2  and .05n/m = .05x10^-9m = x 

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.