Distance and Displacement

Scalar quantities:

• Have magnitude (size) but no direction.

• Examples: distance (10m) time (6 s) speed (12.3 km/h)

Vector quantities:

• Have both magnitude (size) and direction.

• Examples: * position (12 km due south)

* displacement ( 3m upward)

* velocity ( 13.5 m/s downward)

Distance and Displacement

•Distance and displacement are two quantities which may seem to mean the same thing, yet they have distinctly different meanings and definitions.

•Distance (d) is a scalar quantity which refers to "how far an object has moved" during its motion.

•Displacement (d) is a vector quantity which refers to the object's change in position.

Position

• Location of the object at a specific time

displacement = Positionfinal - Positioninital

Example A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

• Even though the physics teacher has walked a total distance of 12 meters, her displacement is 0 meters.

• During the course of her motion, she has "covered 12 meters of ground" (distance = 12 m).

• Yet, when she is finished walking, she is not "out of place" – i.e., there is no displacement for her motion (displacement = 0 m). Displacement, being a vector quantity, must give attention 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.

Example:

• Tommy walks from home (0m) to school which is 4.55 m North of his house. What is his displacement?

• ∆d = df – di

= 4.55m – 0m

= 4.55 m N or +4.55m

Example:

• A dog escapes from his owner’s house and finds a garden to dig up 21 m east of his house. He is scared off by a cat and ends up under a tree 6.5 m east of his house. What is his displacement?

• ∆d = df – di = 6.5 m – 21m

= -14.5 m (or 14.5 m west)

Some examples of vector addition….