Motion in One Dimension

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 VS Displacement Distance (d) is a scalar quantity which refers to "how far an object has moved" during its motion. Displacement (x) is a vector quantity which refers to the object's change in position.

Frame of Reference Frame of reference is a place or object that you assume is fixed observations of how objects move in relation to that frame of reference. perception of motion depends on the observers frame of reference.

Position Location of the object at a specific time displacement = Positionfinal - Positioninital ∆ x = xf -xi

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).

Displacement Vs distance

Distance vs. Displacement

Distance: Displacements Along a Line

Distance: Displacements Along a Line

Example: Tommy walks from home (0m) to school which is 4.55 m North of his house. What is his displacement? ∆x = xf – xi = 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 runs back towards his house and ends up 6.5 m west of the garden. What is his displacement? ∆x = xf – xi = 6.5 m – 21m = -14.5 m (or 14.5 m east)

Vectors

Steps in solving distance/displacement problems Draw a diagram What are they asking for? Use the correct formula Don’t forget units (it’s wrong if there are no units) Include directions only if it is displacement.