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Distance and Displacement
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Procedure•Draw a dot at the intersection of two lines
near the bottom edge of a sheet of graph paper. Label the dot “Start”.
•Draw a second, similar dot near the top of the paper. Label this dot “End”.
•Draw a path from the Start dot to the End dot. Choose any path that stays on the grid lines.
•Use a ruler to determine the distance of your path.
•This is the distance
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Procedure 2
•Now draw a line directly from start to finish.
•Measure this distance with your ruler.•This is the displacement
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Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.
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Example
Consider the motion depicted in the diagram below. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.
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Example
•Even though the physics teacher has walked a total distance of 12 meters, his displacement is 0 meters. During the course of motion, he has "covered 12 meters of ground" (distance = 12 m).
•Yet when he is finished walking, she is not "out of place" - i.e., there is no displacement for her motion (displacement = 0 m).
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What is the displacement of the cross-country team if they begin at the school, run 10 miles and finish back at the school?
The displacement of the runners is 0 miles. While they have covered a distance of 10 miles, they are not "out of place" or displaced. They finish where they started. Round-trip motions always have a displacement of 0.
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What is the distance and the displacement of the race car drivers in the Daytona 500?
Distance: 500 milesDisplacement: 0
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Scalar vs. Vector
•Scalars are quantities that are fully described by a magnitude (or numerical value) alone.
•Vectors are quantities that are fully described by both a magnitude and a direction.
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Scalar or Vector?A. 5 m
B. 30 m/sec, East
C. 5 mi., North
D. 20 degrees Celsius
E. 256 bytes
F. 4000 Calories
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Scalar or Vector?A. 5 m
▫ScalarB. 30 m/sec, East
▫VectorC. 5 mi., North
▫VectorD. 20 degrees Celsius
▫ScalarE. 256 bytes
▫ScalarF. 4000 Calories
▫Scalar
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Displacement (x)
Straight line distance from the initial position to the final position (change in position)
Can be positive or negative
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Displacement• What is the
displacement for the objects shown?
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Displacement• What is the
displacement for the objects shown?
• Answer: 70 cm
• Answer: -60 cm
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Algebra Review
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3a + 8 = 32
a = 8
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3c + 5 = 23
c = 6
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d/4 + 8 = 16
d = 32
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f = 45
f = 81
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f + 36 = 117
f = 145.8