A thin block of soft wood with a mass of 0.0820 kg rests on a horizontal frictionless surface. A bullet with a mass of 4.67 g is fired with a speed of 500 m/s at a block of wood and passes completely through it. The speed of the block is 16.0 m/s immediately after the bullet exits the block.
(a) Determine the speed of the bullet as it exits the block.
(b) Calculate the initial and final kinetic energies of the system.

50 meters per 5 seconds

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. 

'b ' is the correct conclusion.