Kinematic Concepts - Mission KC2 Detailed Help

A football coach starts at the 10-yard line (A) and walks to the 40-yard line (B) in 3 minutes. He turns around and walks to the 0-yard line (C) in the next 2 minutes. He turns around again and walks back to the 50-yard line (D) in the next three minutes. He turns around once more and walks back to the 25-yard line (E) in the next two minutes, thus completing his 10 minutes of pacing. The coach's overall displacement is ____.

 
Definition of Displacement:
The displacement of a moving object is the overall change in position of the object.


 
Displacement is a vector quantity which is always conscious of the direction of motion and any changes in that direction. Distance is a scalar quantity which is ignorant of the direction of travel and any changes in direction. Suppose that a person walks 12 meters, east and then 4 meters, west. The distance traveled is 16 meters. The displacement of the object is 8 meters, east. The fact that there is a direction change must be considered when measuring the displacement. Displacement must account for the fact that the 4 meter segment of the motion was in the opposite direction of the 12 meters. For the displacement measurement, the 4 meters is considered as a negative (a directional adjective) and added onto the +12 meters.

 
Displacement is simply the overall change in position of the object. For a multi-leg trip such as this one, it can be determined by adding all the individual displacements (direction included) for each leg of the trip. But there is a far better way! Being the overall change in position, the displacement can be determined by simply determining how far out of place the final position is from the initial position. Consider only beginning and end positions and find the difference between these two positions. Include direction in your answer since displacement is a vector.