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 = Position final - Position inital

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 = d f – d i = 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 = d f – d i = 6.5 m – 21m = m (or 14.5 m west)

Some examples of vector addition….