Speed
Jean Brainard, Ph.D.
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Printed: July 14, 2014
AUTHOR
Jean Brainard, Ph.D.
www.ck12.org
C HAPTER
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Chapter 1. Speed
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Speed
Define speed, and give the SI unit for speed.
Show how to calculate average speed from distance and time.
Describe instantaneous speed.
Show how to calculate distance or time from speed when the other variable is known.
Did you ever play fast-pitch softball? If you did, then you probably have some idea of how fast the pitcher throws
the ball. For a female athlete like the one in the opening image, the ball may reach a speed of 120 km/h (about 75
mi/h). For a male athlete, the ball may travel even faster. A fast-pitch pitcher uses a “windmill” motion to throw the
ball. This is a different technique than other softball pitches, and it explains why the ball travels so fast.
Introducing Speed
How fast or slow something moves is its speed. Speed determines how far something travels in a given amount of
time. The SI unit for speed is meters per second (m/s). Speed may be constant, but often it varies from moment to
moment.
Average Speed
Even if speed varies during the course of a trip, it’s easy to calculate the average speed by using this formula:
speed =
distance
time
For example, assume you go on a car trip with your family. The total distance you travel is 120 miles, and it takes 3
hours to travel that far. The average speed for the trip is:
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120 mi
3h
= 40 mi/h
speed =
Q: 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 41 hour to make the round trip.
What was her average speed for the entire trip? (Hint: The round-trip distance is 6 km.)
A: Terri’s speed can be calculated as follows:
6 km
0.25 h
= 24 km/h
speed =
Instantaneous Speed
When you travel by car, you usually don’t move at a constant speed. Instead you go faster or slower depending on
speed limits, traffic lights, the number of vehicles on the road, and 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 the pictures in the Figure 1.1.) You
might come to a complete stop at traffic lights, slow down as you turn corners, and speed up to pass other cars.
Therefore, your speed at any given instant, or your instantaneous speed, may be very different than your speed at
other times. Instantaneous speed is much more difficult to calculate than average speed. If you want to learn more
about calculating speed, watch the video at this URL:
http://www.youtube.com/watch?v=a8tIBrj84II
FIGURE 1.1
Cars race by in a blur of motion on an
open highway but crawl at a snail’s pace
when they hit city traffic.
Calculating Distance or Time from Speed
If you know the average speed of a moving object, you can calculate the distance it will travel in a given period of
time or the time it will take to travel a given distance. To calculate distance from speed and time, use this version of
the average speed formula given above:
distance = speed × time
For example, if a car travels at an average speed of 60 km/h for 5 hours, then the distance it travels is:
distance = 60 km/h × 5 h = 300 km
To calculate time from speed and distance, use this version of the formula:
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Chapter 1. Speed
time =
distance
speed
Q: If you walk 6 km at an average speed of 3 km/h, how much time does it take?
A: Use the formula for time as follows:
distance
speed
6 km
=
3 km/h
=2h
time =
Summary
• How fast or slow something moves is its speed. The SI unit for speed is meters per second (m/s).
• Average speed is calculated with this formula:
speed =
distance
time
• Speed may be constant, but often it varies from moment to moment. Speed at any given instant is called
instantaneous speed. It is much more difficult to calculate than average speed.
• Distance or time can be calculated by solving the average speed formula for distance or time.
Vocabulary
• speed: How quickly or slowly something moves; calculated as distance divided by time.
Practice
Do problems 1–3 on the average speed worksheet at the following URL.
http://www.mrjgrom.com/Physics%20resources/Speed_Problem_hw1.pdf
Review
1.
2.
3.
4.
What is speed?
If you walk 3 kilometers in 30 minutes, what is your average speed in kilometers per hour?
Compare and contrast instantaneous and average speed.
What distance will a truck travel in 3 hours at an average speed of 50 miles per hour?
References
1. Left: Kenny Louie; Right: Mario Roberto Duran Ortiz. Cars on a highway have a greater speed than cars in
city traffic. Left: CC BY 2.0; Right: CC BY 3.0
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