Distance and Displacement

Despicable Me: Vector

Guiding Questions What are scalar and vector quantities? What is frame of reference? What is distance? How is displacement different from distance? Guiding Questions

A vector is described by magnitude (size) and direction Scalar A vector is described by magnitude (size) and direction Example.. Where is Big Spring? 40 mi, East A scalar is described by magnitude (size) only Example…How fast is the speed limit? 70 mph

Displacement Velocity Acceleration Force Lift Momentum Mass Length Vector Scalar Displacement Velocity Acceleration Force Lift Momentum Mass Length Volume Density Energy Speed

Frame of Reference How do you know an object is moving? A frame of reference is a set of coordinates that can be used to determine positions and velocities of objects in that frame; different frames of reference move relative to one another. Frame of Reference

Distance Length of a path between two points SI unit is Meters (m) What are some other units of distance

Displacement Displacement is a vector- it has a size and direction. Same units as distance but includes direction. Ex: 5 miles East What is Billy’s displacement? Distance? Displacement

Distance vs Displacement Distance is a scalar quantity which refers to “the amount of ground an object has covered" during its motion. Displacement is a vector quantity which refers to the overall change in position of the object from start to finish. Distance vs Displacement

Displacement vs. Distance An athlete runs around a track that is 100 meters long three times, then stops. What is the athlete’s distance and displacement? Distance = 300 m Displacement = 0 m Why?

What is the distance the physics student travelled What is the distance the physics student travelled? What is their displacement? A student walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The student covered a distance of 12 m (4m + 2m + 4m +2 m) = 12 meters and has a displacement of O m

Challenge: Pythagoras What happens when a person walk 4m east, turns and walks 2m north then stops. Can you find displacement? Pythagoras: a2+b2=c2 42+22 = c2 20=c2 4.4 = c 2 meters 4 meters

Review What is the distance and the displacement of the race car drivers in the Indy 500? The displacement of the cars is somewhere near 0 miles since they virtually finish where they started. Yet the successful cars have covered a distance of 500 miles.

Why does it matter? Travel Taxis: driver should operate such that distance is as close to displacement as possible…otherwise you’re being taken on the scenic (and more expensive) route Directions: a kind local informing you that the museum you’ve been searching for is “only a few blocks from here” doesn’t help unless they include direction So what? When would someone need to know the difference between distance and displacement? Other ex Airplane layovers, Ambulance, Train, Road, Subway, etc. Animal migration Plug-in appliances (length of extension cord is usually greater than displacement from outlet) 06/14/05