Distance & Displacement

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Distance & Displacement How much did you travel from your house to your friend’s house? 8.2 km + 1.8 km + 4.5 km = 14.5 km so, distance is 14.5 km. Where is your friend’s house located as compared to your house? 2.7 km at 4o W of N so, displacement is 2.7 km at 356o E of N

What is a Vector? A vector is an arrow. A vector has a starting point (Tail) and an ending arrow(Head) . Head magnitude Ɵ Tail reference direction A vector has magnitude (size) and direction (angle in o formed with a reference direction).

Distance & Displacement Distance is the length of the actual path taken by an object. Consider travel from point A to point B in diagram below: Distance d is a scalar quantity (no direction): A B d = 20 m Contains magnitude only and consists of a number and a unit. (20 m, 40 mi/h, 10 gal)

Displacement—A Vector Quantity Displacement is the straight-line separation of two points in a specified direction. N A vector quantity: Contains magnitude AND direction, a number, unit & angle. (12 m, 200 N of E) A B D = 12 m, 20o q E

Distance & Displacement Displacement is the straight-line separation of two points in a specified direction (arrow). A vector quantity: Contains magnitude AND direction, a number, unit & angle. (12 m, 300; 8 km/h, N) A B d = 12 m, 20o q

Q: Displacement vs. distance. 𝜃 1. What is distance? distance=4 + 3 +4 = 11 blocks 2. What is displacement (magnitude & angle)? 𝑅= 8 2 + 3 2 ≅8.5 𝑏𝑙𝑜𝑐𝑘𝑠 𝜃= 𝑡𝑎𝑛 −1 3 8 = 21 𝑜 𝑡𝑎𝑛𝜃= 𝑜𝑝𝑝. ℎ𝑦𝑝. = 3 8 N of E

Distance & Displacement For motion along x or y axis, the displacement is determined by the x or y coordinate of its final position. Example: Consider a car that travels 8 m, E then 12 m, W. Net displacement d is from the origin to the final position: d 8 m,E x x = -4 x = +8 d = 4 m, W 12 m,W What is the distance traveled? 20 m !!