# Paths in One and Two Dimensions 1-1-1 Displacement and Distance.

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Paths in One and Two Dimensions 1-1-1 Displacement and Distance

SCALAR –A measured quantity that has NO DIRECTION –Examples Distance, Time, Mass, Volume VECTOR –A measured quantity that includes DIRECTION –SIGN SHOWS DIRECTION –Example Displacement Scalar vs. Vector

Displacement vs. Distance DISTANCE –The complete length of the path traveled by a moving object Distance 219 mi Displacement 168 mi DISPLACEMENT –the length of the straight-line path from a moving object’s origin to its final position New York to Boston

A ball rolls 5 meters north. Distance = Displacement = 5 m +5 m Sign Conventions Positive UP NORTH EAST RIGHT Negative DOWN SOUTH WEST LEFT A cat runs 8 meters west. Distance = Displacement = A bird flies 5 meters north, then 7 meters south Distance = Displacement = 8 m -8 m 12 m -2 m

Example #1 A man drives his car 3 miles north, then 4 miles east. What distance did he travel? What is his displacement from his point of origin? 3 mi North 4 mi East Displacement 5 mi Direction? Distance 7 mi

Example #2 Three men leave the same house on foot. The first man walks 30 feet north, then 40 feet west. The second man walks 90 feet south, then 88 feet north. The third man walks 10 feet east, then 50 feet west. Which man has traveled the greatest distance? Who is farthest from the house? Who is closest to the house? The second man The first man The second man

Distance vs. Time Graphs During what time interval was the object NOT MOVING? 2 – 3 seconds The interval on the graph where the distance remains constant!

Displacement vs. Time Graphs When the displacement is negative, the object has a position to the left of the origin 1 – 2 and 4 – 5 seconds Constant displacement means that the object doesn’t move The object’s final position is at +1 meter (1 meter to the right of the origin) During what time interval(s) was the object to the left of the origin? During what time interval(s) was the object NOT MOVING? At what distance from the origin does the object stop?

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