Distance & Displacement

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