# speed and velocity

## distancetime graphs

The motion of an object can be represented by a distance-time graph like the one in Figure 12.8. A distance-time graph shows how the distance from the starting point changes over time. The graph in Figure 12.8 represents a bike trip. The trip began at 7:30 AM (A) and ended at 12:30 PM (F). The rider traveled from the starting point to a destination and then returned to the starting point again.

## instantaneous vs. average speed

When you travel by car, you usually dont move at a constant speed. Instead you go faster or slower depending on speed limits, traffic, traffic lights, and many other factors. For example, you might travel 65 miles per hour on a highway but only 20 miles per hour on a city street (see Figure 12.7). You might come to a complete stop at traffic lights, slow down as you turn corners, and speed up to pass other cars. The speed of a moving car or other object at a given instant is called its instantaneous speed. It may vary from moment to moment, so it is hard to calculate. Its easier to calculate the average speed of a moving object than the instantaneous speed. The average speed is the total distance traveled divided by the total time it took to travel that distance. To calculate the average speed, you can use the general formula for speed that was given above. Suppose, for example, that you took a 75-mile car trip with your family. Your instantaneous speed would vary throughout the trip. If the trip took a total of 1.5 hours, your average speed for the trip would be: average speed = 75 mi = 50 mi/h 1.5 h You can see a video about instantaneous and average speed and how to calculate them at this URL: MEDIA Click image to the left or use the URL below. URL: You Try It! Problem: Terri rode her bike very slowly to the top of a big hill. Then she coasted back down the hill at a much faster speed. The distance from the bottom to the top of the hill is 3 kilometers. It took Terri 15 minutes to make the round trip. What was her average speed for the entire trip?

## speed

Speed is an important aspect of motion. It is a measure of how fast or slow something moves. It depends on how far something travels and how long it takes to travel that far. Speed can be calculated using this general formula: speed = distance time A familiar example is the speed of a car. In the U.S., this is usually expressed in miles per hour (see Figure 12.6). If your family makes a car trip that covers 120 miles and takes 3 hours, then the cars speed is: speed = 120 mi = 40 mi/h 3h The speed of a car may also be expressed in kilometers per hour (km/h). The SI unit for speed is meters per second (m/s).

## velocity

Speed tells you only how fast an object is moving. It doesnt tell you the direction the object is moving. The measure of both speed and direction is called velocity. Velocity is a vector that can be represented by an arrow. The length of the arrow represents speed, and the way the arrow points represents direction. The three arrows in Figure directions. They represent objects moving at the same speed but in different directions. Vector C is shorter than vector A or B but points in the same direction as vector A. It represents an object moving at a slower speed than A or B but in the same direction as A. If youre still not sure of the difference between speed and velocity, watch the cartoon at this URL: (2:10). MEDIA Click image to the left or use the URL below. URL: In general, if two objects are moving at the same speed and in the same direction, they have the same velocity. If two objects are moving at the same speed but in different directions (like A and B in Figure 12.9), they have different velocities. If two objects are moving in the same direction but at a different speed (like A and C in Figure 12.9), they have different velocities. A moving object that changes direction also has a different velocity, even if its speed does not change.

## calculating distance from speed and time

If you know the speed of a moving object, you can also calculate the distance it will travel in a given amount of time. To do so, you would use this version of the general speed formula: distance = speed time For example, if a car travels at a speed of 60 km/h for 2 hours, then the distance traveled is: distance = 60 km/h 2 h = 120 km You Try It! Problem: If Maria runs at a speed of 2 m/s, how far will she run in 60 seconds?

## slope equals speed

In a distance-time graph, the speed of the object is represented by the slope, or steepness, of the graph line. If the line is straight, like the line between A and B in Figure 12.8, then the speed is constant. The average speed can be calculated from the graph. The change in distance (represented by Dd) divided by the change in time (represented by Dt): speed = Dd Dt For example, the speed between A and B in Figure 12.8 is: speed = Dd 20 km 0 km 20 km = = = 20 km/h Dt 8:30 7:30 h 1h If the graph line is horizontal, as it is between B and C, then the slope and the speed are zero: speed = Dd 20 km 20 km 0 km = = = 0 km/h Dt 9:00 8:30 h 0.5 h You Try It! Problem: In Figure 12.8, calculate the speed of the rider between C and D.

## instructional diagrams

No diagram descriptions associated with this lesson

## questions

When calculating average speed, the symbol d represents the

``````-->  a. change in distance.

b. change in direction.

c. instantaneous distance.

d. division of distance by time.
``````

Speed depends on how far something travels and

``````a. how steep its route is.

b. which direction it travels.

-->  c. how much time it takes to travel that far.

d. none of the above
``````

If you run a 100-meter race in 20 seconds, what is your average speed during the race?

``````a. 20 m/s

b. 10 m/s

-->  c. 5 m/s

d. 2 m/s
``````

What is the SI unit for speed?

``````a. s

b. m

-->  c. m/s

d. s/m
``````

Tony ran at a constant speed of 10 m/s for a total of 60 seconds. How far did he run?

``````a. 6m

b. 60 m

-->  c. 600 m

d. 6000 m
``````

If the slope of a distance-time graph is steep, then the speed of the object must be

``````a. slow.

-->  b. rapid.

c. constant.

d. changing.
``````

If you travel 500 kilometers in 5 hours, your average speed is

``````a. 5 km/h

b. 50 km/h

-->  c. 100 km/h

d. 250 km/h
``````

If you use an arrow to represent velocity, what does the length of the arrow represent?

``````a. time

-->  b. speed

c. distance

d. direction
``````

Which choice(s) could represent the velocity of a moving car?

``````a. 80 mi/h

b. 40 km/h

-->  c. 50 km/h north

d. all of the above
``````

Objects moving at the same velocity have the same

``````a. size.

b. speed.

c. direction.

-->  d. two of the above
``````

Which quantity is a vector?

``````a. speed

-->  b. velocity

c. direction

d. distance
``````

If speed is constant, velocity

``````a. must be zero.

b. must be constant.

-->  c. can be changing.

d. none of the above
``````

Both speed and velocity are vectors.

``````a. true

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

The symbol t represents a change in time.

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

b. false
``````

The length of a velocity arrow represents distance.

``````a. true

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

A straight line on a distance-time graph means that speed is zero.

``````a. true

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

Speed is negative when an object moves backward.

``````a. true

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

Speed depends on both distance and direction.

``````a. true

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

It is easier to calculate average speed than instantaneous speed.

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

b. false
``````

The slope of a distance-time graph represents the direction of motion.

``````a. true

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

Velocity is the scientific term for speed.

``````a. true

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

Speed can only be greater than or equal to zero.

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

b. false
``````

Objects moving at the same speed always have the same velocity.

``````a. true

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

Average speed can be calculated from a distance-time graph.

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

b. false
``````

Speed equals distance multiplied by time.

``````a. true

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

A change in speed can occur without a change in velocity.

``````a. true

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

A change in velocity can occur without a change in speed.

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

b. false
``````

measure of both speed and direction

``````a. speed

-->  b. velocity

c. instantaneous speed

d. average speed

e. slope

f. distance

g. time
``````

distance speed

``````a. speed

b. velocity

c. instantaneous speed

d. average speed

e. slope

f. distance

-->  g. time
``````

speed of a moving object at a given moment

``````a. speed

b. velocity

-->  c. instantaneous speed

d. average speed

e. slope

f. distance

g. time
``````

speed time

``````a. speed

b. velocity

c. instantaneous speed

d. average speed

e. slope

-->  f. distance

g. time
``````

general term for how quickly or slowly something moves

``````-->  a. speed

b. velocity

c. instantaneous speed

d. average speed

e. slope

f. distance

g. time
``````

total distance traveled divided by the time it took to travel that distance

``````a. speed

b. velocity

c. instantaneous speed

-->  d. average speed

e. slope

f. distance

g. time
``````

steepness of a graph line

``````a. speed

b. velocity

c. instantaneous speed

d. average speed

-->  e. slope

f. distance

g. time
``````

## diagram questions

No diagram questions associated with this lesson