Distance & Displacement
Feb 15, 2016
Distance & Displacement
Distance is a Scalar
•A measure of the length of a path an object takes in moving from one position to another is called distance.
•Distance is how far an object has moved•Distance is a scalar quantity.
Distance
• Distance (d) = how far an object travels.– Does not depend on direction.
• Imagine an ant crawling along a ruler.
• What distance did the ant travel?d = 3 cm
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Distance
• Distance does not depend on direction.
• Now what distance did the ant travel?d = 3 cm
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Distance
• Distance does not depend on direction.• Follow the ant again:
• What distance did the ant walk this time?• d = 7 cm
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Displacement is a Vector
• Displacement is the change in position of an object and includes a description of the direction of motion.
• Determined by drawing a straight line from starting position to ending position
• Is not always equal to distance traveled.
Displacement
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Displacement• Displacement has direction.
• Distance: 3 cm• Displacement: +3 cm
The positive gives the ant a direction
Displacement
• Find the ant’s displacement again.
• Distance: 3 cm• Displacement: -3 cm
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Displacement
• Find the distance and displacement of the ant.
• Distance: 7 cm• Displacement: +3 cm• = 5cm – 2cm = +3cm
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QUESTION: How far (in km) will a car travel in 15 min at 20 m/s ?
d = s x t= (20 m) x (60 s) (15 min)
s min
= 18 000 m (divide 1000 for km) = 18 km
Displacement
E.g. the distance travelled here by a driver was 14.5 km even though the displacement was only 2.7 km [North].
•E.g If a person travels 40m east, turns and travels 30m west, the displacement of the person is 10m east.
•If a person travels 40m east and then travels another 50m east, the displacement is 90m east.
Displacement
Example: Mandisa walks 2 m [East] and then 1 m [West]. What was her distance travelled?What was her displacement?
Distance travelled: Dd = 2 m + 1 m = 3 mDisplacement:
She is 1 m [East] of her original starting position.1 m1 m
Displacement
We can represent [East] as the positive direction and [West] as the negative direction:
= 2 m [East] + 1 m [West]= + 2 m – 1 m= + 1 m= 1 m [East]
2 m
1 m1 m
Distance: How far something travels
What is the difference between distance and displacement?
Displacement: How far something travels in a given direction in a straight line from start to finish.
• A soccer player changes position back and forth on the field. In the diagram below each position is marked where the player reverses direction. The player moves from position A to B to C to D.
• Find the distance and displacement of travel.
Solution:
Distance = 85 m
Displacement = 55 m left of A
Displacement
• Therefore, displacement = difference between an object’s final position and its starting position.– Does depend on direction.
• Displacement = final position – initial position
• Examples of directions:– + and –– N, S, E, W– Angles
Displacement vs. Distance
• Example of distance:– The car drove 30 km.
• Example of displacement:– The car drove 30 km. EAST.
• An object’s distance traveled and its displacement aren’t always the same!
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?
• Complete worksheet