PLEASE HELP ME WITH THIS ONE QUESTION You have 1 kg of water and you want to use that to melt 0.1 kg of ice. What is the minimum temperature necessary in the water, to just barely melt all of the ice? (Lf = 3.33 x 105 J/kg, cwater 4186 J/kg°C)

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.