It takes 3.62 J of heat to raise the temperature of Object A by 1 C, and 3.02 J to raise the temperature of Object B by 1 C. Suppose A and B are brought into contact. A is initially hotter. A is seen to cool down by 14.3 C. How would you calculate the rise in temperature of B

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. 

Need more information like a picture