September 4, 2014

I will be expected to know the difference between vector and scalar values and what types of quantities are vectors and scalars.

Distance & Displacement

Distance & Displacement Distance and displacement are two

quantities which may seem to mean the same thing, yet have distinctly different definitions and meanings

Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion.

Distance & Displacement Displacement is a vector quantity

which refers to "how far out of place an object is"; it is the object's change in position.

Recall that a scalar has only a magnitude (an amount) and a vector is described by both a magnitude and a direction

Distance & Displacement To test your understanding of this distinction,

consider the following motion depicted in the diagram below. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

startfinish

Distance & Displacement Even though the physics teacher has

walked a total distance of 12 meters, his displacement is 0 meters. During the course of his motion, he has "covered 12 meters of ground" (distance = 12 m).

startfinish

Distance & Displacement

Yet, when he is finished walking, he is not "out of place" - i.e., there is no displacement for his motion (displacement = 0 m). Displacement, being a vector quantity, must give attention and regard to direction. The 4 meters east is canceled by the 4 meters west; and the 2 meters south is canceled by the 2 meters north.

finishstart

Distance & Displacement Picture the movement of the teacher on a

piece of graph paper. If the teacher moves up or to the right, his

movement is positive If the teacher moves down or to the left, his

movement is negative

Distance & Displacement

Now for a final example. Seymour views football games from under the bleachers. He frequently paces back and forth to get the best views. The diagram below shows several of Seymour's positions at various times. At each marked position, Seymour makes a "U-turn" and moves in the opposite direction.

Distance & Displacement In other words, Seymour moves from

position A to B to C to D. What is Seymour's resulting displacement and distance of travel?

Distance & Displacement Seymour’s distance is 95 yards He traveled 35 yards from point A

to point B. He then traveled 20 yards from

point B to point C. Finally he traveled 40 yards from

point C to point D.

Distance & Displacement Seymour has a displacement of –

55 yards He travels –35 yards left from point

A to point B. He then travels +20 yards to the

right from point B to point C. Finally he travels –40 yards to the

left from point C to point D.