An object of unknown mass is initially at rest and dropped from a height h. It reaches the ground with a velocity v1 v 1 . The same object is then raised again to the same height h but this time is thrown downward with velocity v1 v 1 . It now reaches the ground with a new velocity v2 v 2 . How is v2 v 2 related to v1 v 1 ?

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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.