Adesigner wishes to use a stepper motor coupled to a gearbox to drive an indexed conveyor belt to achieve a linear resolution of 1 mm and a maximum speed of 10 cm/sec. the gearbox is a speed reducer with a gear ratio of 3 to 1, and the conveyor is driven by a 10-cm diameter drum attached to the output shaft of the gearbox. what is the minimum resolution required for the stepper motor

Scissors and a seesaw both cut things that’s the only comparison

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.