A 15 Watt desk-type fluorescent lamp has an effective resistance of 200 ohms when operating (note: the 15 Watts is only associated with the lamp). It is in series with ballast that has a resistance of 80 ohms and an inductance of .9H. The lamp and ballast are operated at 120V, 60HZ. Draw the circuit Calculate the power drawn by the lamp (hint: for R use the sum of both

a. resistances)
b. Calculate the apparent power
c. Calculate the power factor
d. Calculate the reactive power Calculate the size of the capacitor necessary to provide unity power factor

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. 

Ibelieve the answer is d. macula  hope my answer has you : )

Ithink the answer is c. make unnecessarily  wide gestures