Physics 1
Kinematics Notes
Average Speed

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Average Speed

The average speed of an object tells you the (average) rate at which it covers distance. If a car's average speed is 65 miles per hour, this means that the car's position will change (on the average) by 65 miles each hour.

Average speed is a rate. In kinematics, a rate is always a quantity divided by the time taken to get that quantity (the elapsed time). Since average speed is the rate position changes, average speed = distance traveled/time taken.

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Example:

A car travels between 2 towns 60 miles apart in 2 hours. What is its average speed?

Answer:

average speed = distance/time Therefore, the average speed of the car is 60 miles/2 hours = 30 miles/hour.

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Example:

If a person can walk with an average speed of 2 meters/second, how far will they walk in 4 minutes?

Answer:

There are 60 seconds in 1 minute, so there are 4 (60 seconds) = 240 seconds in 4 minutes. Also, if average speed = distance/time, then distance = (average speed)(time). Therefore, the distance the person moves is (2 m/s)(240 s) = 480 meters.

Speed Units

Since average speed is always calculated as a distance (length) divided by a time, the units of average speed are always a distance unit divided by a time unit. Common units of speed are meters/second (abbreviated m/s), centimeters/second (cm/s), kilometers/hour (km/hr), miles/hour (mi/hr - try to avoid the common abbreviation mph), and many others.

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Example:

Which of the following could be a speed measurement?

1. 2.5 meters
2. 2.5 seconds/meter
3. 2.5 meters/second
4. 2.5 meters/second/second

Answer:

Only 2.5 meters/second could be a speed measurement. Speed always has units of a distance (length) unit divided by a time unit.

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Which Distance?

Farmer Jones drives 6 miles down a straight road. She turns around and drives 4 miles back. What was her average speed for this trip if it took 1 hour?

Your answer to this problem depends on your interpretation of "distance traveled". You could say:

• The total distance traveled by Farmer Jones is 10 miles. Therefore her average speed is 10 mi/hr.
• The net distance traveled by Farmer Jones is 2 miles. Therefore, her average speed is 2 mi/hr.

There are good reasons to use either interpretation - it's mostly a matter of preference. We will interpret "distance traveled" to be net distance (also called displacement). Farmer Jones' average speed was 2 mi/hr.

NOTE: Different texts may adopt other conventions! In fact, our AP Physics text uses total distance to calculate speed, but net distance to calculate velocity. Use caution here!

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The Perils of Averaging Averages

Here is an interesting problem:

Susie has planned a trip to a city 60 miles away. She wishes to have an average speed of 60 miles/hour for the trip. Due to a traffic jam, however, she only has an average speed of 30 miles/hour for the first 30 miles. How fast does she need to go for the remaining 30 miles so that her average speed is 60 miles/hour for the whole trip?

Most likely you thought "Oh, 90 miles/hour - since the average of 30 and 90 is 60! Boy, this is easy!"

Unfortunately, however, the answer is not 90 miles/hour. Here's why: You know that average velocity = distance/time (v = d/t). In order to have an average speed of 60 miles/hour over a distance of 60 miles, you must complete the trip in 1 hour:

But Susie has already taken an hour (it takes 1 hour to go 30 miles with an average speed of 30 miles/hour) - and she is only half way! It is impossible for her to complete the trip with an average speed of 60 miles/hour! She would have to go infinitely fast!

Notice that it would take 1/3 of an hour to cover the last 30 miles at 90 miles/hour. The total time for her trip would be 1.33 hours, and her average speed would be:

Try this calculation for any speed for the second half of the trip - the average speed for the whole trip cannot ever be 60 miles/hour! The moral of the story: Don't average averages!

Measuring Speed Activity

This would be a good time to do the Measuring Speed Activity, in which you:

• determine some average speeds by measuring distances and times, and
• determine an unknown distance by measuring time to cover the distance at a known speed

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[Chapter 2 Objectives]