paths in one and two dimensions 1-1-1 displacement and distance
TRANSCRIPT
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
Distance219 mi
Displacement168 mi
• DISPLACEMENT – the length of the
straight-line path from a moving object’s origin to its final position
New York to BostonNew York to Boston
A ball rolls 5 meters north.
Distance =
Displacement =
5 m
+5 m
Sign Conventions
PositiveUP
NORTHEAST
RIGHT
NegativeDOWNSOUTHWESTLEFT
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 miNorth
4 miEast
Displacement5 mi
Direction?
Distance7 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 GraphsDuring what time interval was the object NOT MOVING?
Distance vs. Time
0
2
4
6
8
10
12
14
16
18
0 1 2 3 4 5 6 7
Time (s)
Dis
tan
ce (
m)
2 – 3 secondsThe interval on the graph wherethe distance remains constant!
Displacement vs. Time Graphs
Displacement vs. Time
-4
-3
-2
-1
0
1
2
3
4
5
6
0 1 2 3 4 5 6 7
Time (s)
Dis
pla
cem
en
t (m
)
When the displacement isnegative, the object has a
position to the left of the origin1 – 2 and 4 – 5 seconds
Constant displacement means thatthe object doesn’t move
The object’s final position isat +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?