# distance and direction

## si unit for distance

The SI unit for distance is the meter (1 m = 3.28 ft). Short distances may be measured in centimeters (1 cm = 0.01 m). Long distances may be measured in kilometers (1 km = 1000 m). For example, you might measure the distance a frogs tongue moves in centimeters and the distance a cheetah moves in kilometers.

## using maps to measure distance

Maps can often be used to measure distance. Look at the map in Figure 12.4. Find Mias house and the school. You can use the map key to directly measure the distance between these two points. The distance is 2 kilometers. Measure it yourself to see if you agree.

## frame of reference

Assume that a school bus, like the one in Figure 12.2, passes by as you stand on the sidewalk. Its obvious to you that the bus is moving. It is moving relative to you and the trees across the street. But what about to the children inside the bus? They arent moving relative to each other. If they look only at the other children sitting near them, they will not appear to be moving. They may only be able to tell that the bus is moving by looking out the window and seeing you and the trees whizzing by. This example shows that how we perceive motion depends on our frame of reference. Frame of reference refers to something that is not moving with respect to an observer that can be used to detect motion. For the children on the bus, if they use other children riding the bus as their frame of reference, they do not appear to be moving. But if they use objects outside the bus as their frame of reference, they can tell they are moving. What is your frame of reference if you are standing on the sidewalk and see the bus go by? How can you tell the bus is moving? The video at the URL below illustrates other examples of how frame of reference is related to motion. MEDIA Click image to the left or use the URL below. URL:

## distance

Did you ever go to a track meet like the one pictured in Figure 12.3? Running events in track include 100-meter sprints and 2000-meter races. Races are named for their distance. Distance is the length of the route between two points. The length of the route in a race is the distance between the starting and finishing lines. In a 100-meter sprint, for example, the distance is 100 meters.

## direction

Things dont always move in straight lines like the route from Mias house to the school. Sometimes they change direction as they move. For example, the route from Mias house to the post office changes from west to north at the school (see Figure 12.4). To find the total distance of a route that changes direction, you must add up the distances traveled in each direction. From Mias house to the school, for example, the distance is 2 kilometers. From the school to the post office, the distance is 1 kilometer. Therefore, the total distance from Mias house to the post office is 3 kilometers. You Try It! Problem: What is the distance from the post office to the park in Figure 12.4? Direction is just as important as distance in describing motion. For example, if Mia told a friend how to reach the post office from her house, she couldnt just say, "go 3 kilometers." The friend might end up at the park instead of the post office. Mia would have to be more specific. She could say, "go west for 2 kilometers and then go north for 1 kilometer." When both distance and direction are considered, motion is a vector. A vector is a quantity that includes both size and direction. A vector is represented by an arrow. The length of the arrow represents distance. The way the arrow points shows direction. The red arrows in Figure 12.4 are vectors for Mias route to the school and post office. If you want to learn more about vectors, watch the videos at these URLs: (5:27) MEDIA Click image to the left or use the URL below. URL: You Try It! Problem: Draw vectors to represent the route from the post office to the park in Figure 12.4.

## instructional diagrams

No diagram descriptions associated with this lesson

## questions

If motion is represented by an arrow, what does the head of the arrow show?

``````a. speed

b. position

c. distance

-->  d. direction
``````

something that is not moving with respect to an observer that can be used to detect motion

``````a. distance

-->  b. frame of reference

c. motion

d. vector

e. meter

f. direction

g. position
``````

quantity that includes both size and direction

``````a. distance

b. frame of reference

c. motion

-->  d. vector

e. meter

f. direction

g. position
``````

If you were riding in a car down a city street, which frame of reference would not allow you to detect that the car was moving?

``````-->  a. the driver of the car

b. buildings along the street

c. traffic lights at intersections

d. cars parked on the sides of the street
``````

What SI unit would be most appropriate for measuring the distance between Earth and the moon?

``````-->  a. kilometer

b. meter

c. yard

d. mile
``````

location

``````a. distance

b. frame of reference

c. motion

d. vector

e. meter

f. direction

-->  g. position
``````

change in position

``````a. distance

b. frame of reference

-->  c. motion

d. vector

e. meter

f. direction

g. position
``````

Which word could be used to describe the direction of a moving object?

``````a. far

b. fast

c. forever

-->  d. forward
``````

line along which something moves

``````a. distance

b. frame of reference

c. motion

d. vector

e. meter

-->  f. direction

g. position
``````

Frame of reference is

``````-->  a. something that affects perception of motion.

b. a way to represent distance and direction.

c. the line along which something moves.

d. any change of location.
``````

length of the route between two points

``````-->  a. distance

b. frame of reference

c. motion

d. vector

e. meter

f. direction

g. position
``````

SI unit for distance

``````a. distance

b. frame of reference

c. motion

d. vector

-->  e. meter

f. direction

g. position
``````

Direction is as important as distance in describing motion.

``````-->  a. true

b. false
``````

Most foot races are measured in meters.

``````-->  a. true

b. false
``````

Motion is generally defined as an increase in distance.

``````a. true

-->  b. false
``````

Direction is the length of the route between two points.

``````a. true

-->  b. false
``````

Short distances may be measured in centimeters.

``````-->  a. true

b. false
``````

You can use a map to measure the distance between two points.

``````-->  a. true

b. false
``````

A vector is any quantity that has no units of measurement.

``````a. true

-->  b. false
``````

You can measure the distance an object travels only if it does not change direction.

``````a. true

-->  b. false
``````

Motion is a vector when it includes only direction.

``````a. true

-->  b. false
``````

You could measure distances with a metric ruler.

``````-->  a. true

b. false
``````

Speed is one way to measure motion.

``````-->  a. true

b. false
``````

The length of a vector arrow represents direction.

``````a. true

-->  b. false
``````

Words that describe direction include east, up, and left.

``````-->  a. true

b. false
``````

If you were riding on a moving bus, which frame of reference would allow you to detect the motion?

``````a. other people sitting on the bus

-->  b. trees outside the bus windows

c. the seats on the bus

d. the bus driver
``````

Which units would most likely be used to measure the distance between two cities?

``````a. millimeters

b. centimeters

c. meters

-->  d. kilometers
``````

To find the distance of a route that changes direction, you must

``````a. consider only the distance traveled in the first direction.

b. calculate the average distance traveled in one direction.

-->  c. add up all the distances traveled in different directions.

d. subtract the starting distance from the ending distance.
``````

When both distance and direction are considered, motion

``````a. is always measured in meters.

b. cannot be calculated.

c. is a force of nature.

-->  d. is a vector.
``````

To determine the distance between two points on a map, you can use a ruler and

``````a. a compass.

b. the compass rose.

c. a sheet of graph paper.

-->  d. the scale in the map key.
``````

To explain how to get from point A to point B, you must describe both the distance and the

``````a. speed.

b. length.

c. mileage.

-->  d. direction.
``````

## diagram questions

No diagram questions associated with this lesson