Raindrops make an angle q with the vertical when viewed through a moving train window (fig. 3-48). if the speed of the train is vt , what is the speed of the raindrops vd in the reference frame of the earth in which they are assumed to fall vertically?

If θ is the angle the rain makes with the vertical (from the train's reference frame), 

tanθ = (velocity of train) / (velocity of raindrops in Earth frame)

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.