### Unit 1 Day 1 * Displacement v. Distance

```Unit 1 Day 1 –
Displacement v. Distance
Mr. Rana
9/6/12
Bell Ringer (3 min)
Intro (3 min)
If you were driving from
one house to the other,
what would be the
shortest path?
If you were walking
from one house to the
other, what would be
the shortest path?
Which one is the
shorter path?
Distance
• Distance (d) – how far an object travels.
– Does not depend on direction.
• Imagine an ant crawling along a ruler.
0
cm
1
2
3
4
5
6
7
• What distance did the ant travel?
– d = 3 cm
8
9
10
Distance
• Distance does not depend on direction.
• Here’s our intrepid ant explorer again.
0
cm
1
2
3
4
5
6
7
8
• Now what distance did the ant travel?
– d = 3 cm
• Does his direction change the answer?
9
10
Distance
• Distance does not depend on direction.
• Let’s follow the ant again.
0
cm
1
2
3
4
5
6
7
8
• What distance did the ant walk this time?
• d = 7 cm
9
10
Displacement
• Displacement (x) – shortest difference between an
object’s final position and its starting position.
– Does depend on direction.
• Displacement = final position – initial position
• In order to define displacement, we need directions.
• Examples of directions:
– + and –
– N, S, E, W
– Angles
Displacement
displacement.
- +
0
cm
1
2
3
4
5
6
7
8
• Distance: 3 cm
• Displacement: +3 cm
– The positive gives the ant a direction!
9
10
Displacement
• Find the ant’s displacement again.
– Remember, displacement has direction!
- +
0
cm
1
2
3
4
• Distance: 3 cm
• Displacement: -3 cm
5
6
7
8
9
10
Displacement
• Find the distance and displacement of the ant.
- +
0
cm
1
2
3
4
5
• Distance: 7 cm
• Displacement: +3 cm
6
7
8
9
10
Example 1 (5 min)
You walk 20 meters to the bus stop, but you
notice you forgot your homework you run 20
meters back home. With homework in hand you
walk 20 meters to the bus.
Picture:
Displacement:
Distance:
Example 2 (5 min)
• 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?
Guided Practice (10 min)
Example 3 (5 min)
• Dezmond ran 30 meters north, 30 meters
east, 30 meters, south and 30 meters west.
• Picture: Displacement: Distance:
Guided Practice (10 min)
A physics teacher walks 4 meters East, 2 meters
South, 4 meters West, and finally 2 meters
North.
What is the distance traveled?
What is the displacement?
Independent Practice (10 min)
Independent Practice (10 min)
A car is driven from Buffalo to Albany and on to
New York City, as shown in the diagram to the
right. Compared to the size of the car's total
displacement, is distance driven shorter, longer,
or the same? Why?
Independent Practice (10 min)
If you were to pay for gas by the mile, but you
got to choose whether you paid for your mileage
measured by distance or displacement, which
would you choose? Why?
Independent Practice (10 min)
Describe a situation where your distance and
displacement would be the same.
Independent Practice (10 min)
Describe a situation where your distance and
displacement would be different.
Extra
Marshall walks 3 meters north and 4 meters
east. What is his displacement? Distance
traveled?
Fantasia walks 6 blocks south and 8 blocks west.
What is her displacement? Distance traveled?
```