Robin Hood is pursuing a lackey of the Sheriff of Notingham. The lackey hides behind a bale of hay. Robin Hood fires an arrow into the hay and notes that the arrow has only penetrated half way. How much faster must the arrow be fired to go through? If the bow works like a simple spring, how much farther back must he draw the bow to do this, compared to the initial pull?

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.