Name:
Class:
Date:
Time to Roll
Task 1
With a partner, mark off a length of about 1 meter on the floor. Put a
small piece of masking tape at one end and a small piece of masking
tape at the other end. One of you should start rolling a ball towards the
first piece of tape. When the ball reaches the first piece of tape, the
second person should begin counting, as in “one thousand one, one
thousand two, ....” Stop counting when the ball reaches the second
piece of tape.
Record your time here:
Now do a calculation. Divide the distance the ball traveled (1 meter) by
the time it took to travel that distance (however many seconds you
counted).
distance ball traveled
time to travel that distance
=
Task 2
This is a lot like Task 1, with a slight change. This time just place one
piece of masking tape on the floor. One partner rolls the ball toward
the piece of tape. The second partner begins counting, as before, when
the ball reaches the piece of tape. Continue counting until the ball
stops rolling.
Adapted from Companion Classroom Activities for Stop Faking It: Force & Motion
Copyright © 2011 NSTA
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Record your time here:
Measure the total distance the ball traveled in meters.
Record your distance here:
Time for another calculation. Divide the distance the ball traveled (the
distance you measured) by the time it took for the ball to travel that
distance (however many seconds you counted).
distance ball traveled
time to travel that distance
=
Adapted from Companion Classroom Activities for Stop Faking It: Force & Motion
Copyright © 2011 NSTA
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Name:
Class:
Date:
Describing Motion
In the activity Time to Roll, you timed how long it took a ball to travel a
couple of different distances. The first distance was 1 meter. The time
it took your ball to travel one meter could have been anywhere from ¼
of a second to 2 seconds. It all depends on how fast you rolled the ball.
After doing the timing, you divided the distance traveled (1 meter) by
how long it took to travel that distance. In doing that calculation, you
determined the ball’s speed. In fact, that’s how we define speed.
=
Speed
distance an object travels
time to travel that distance
So, suppose it took your ball one second to travel one meter. Then you
would calculate the speed as
Speed
of
ball
=
distance an object travels
time to travel that distance
=
1 meter
1 second
=
m
1
s
This can also be written as 1 m/s.
If it took your ball 2 seconds to travel that one meter, then the speed of
the ball would be
Speed
of ball
=
distance an object travels
time to travel that distance
=
1 meter
2 second
=
m
0.5
s
This can also be written as 0.5 m/s.
Notice that you don’t just use a number for the speed, such as 1, 2, 0.5,
or 7. There are units attached to the number, in this case
meters/second (stated “meters per second”). You’ve no doubt dealt
with speeds before. Car speeds in the United States are measured in
miles/hour rather than meters/second. In other countries, car speeds
are measured in kilometers/hour. Whatever object you’re talking
about, though, the units you measure speed in are a distance divided by
a time. By comparing speeds, you can compare how fast or slow
objects are moving. Clearly, a plane traveling at a speed of 500
Adapted from Companion Classroom Activities for Stop Faking It: Force & Motion
Copyright © 2011 NSTA
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miles/hour is moving a lot faster than a bicycle traveling at 20
miles/hour.
Now, measuring speeds in different units can make comparisons
difficult. Is a ball traveling at 1 meter/second traveling faster or slower
than a car going down the street at 20 miles/hour? It’s not easy to tell
without using the same units. We’re not going to spend time
comparing speeds with different units right now. Just be aware that the
units are important. You should always have units attached to things
like speeds. If you say something is moving at a speed of 10, that
doesn’t tell you much. That could be 10 kilometers/second (really fast!)
or 10 meters/hour (really slow!).
On Being Average
After calculating the speed of the ball that traveled 1 meter, you did the
same calculation for a ball that rolled to a stop. Chances are the speed
you got in this second case was pretty close to the speed you got for the
ball traveling 1 meter. So what’s up with that? Let’s say you got a
speed of 1 meter/second in the situation where the ball rolled to a stop.
Was the ball rolling at that speed the entire time? If not, when was the
ball going that speed? At the beginning? At the end? Well, clearly not
at the end, because at that point the ball was at rest, and its speed was
0 meters/second. And when the ball went by the first piece of tape, it
was probably traveling faster than 1 meter/second. So what’s the
meaning of that speed of 1 meter/second? The speed you calculated
was the average speed of the ball during that entire time. At any
particular time, the ball was traveling at a speed different from the
average speed. If the average speed was 1 meter/ second, then the
speed it was traveling at the start was probably something like 2
meters/second. Later maybe it was traveling at 1.5 meters/second.
Just before it stopped, it might have been traveling at 0.2
meters/second. And when it stopped, it was traveling at 0
meters/second. See Figure 1.
So, there are two kinds of speed. One is the average speed (the total distance traveled divided by the
total time it took to travel that distance) and the other is the instantaneous speed (the speed
something is traveling at a particular point in time).
Adapted from Companion Classroom Activities for Stop Faking It: Force & Motion
Copyright © 2011 NSTA
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Let’s say you’re walking to school. You leave your house traveling at a
speed of 0.5 meters/second and walk at that speed for 5 minutes (300
seconds). Then you stop and pet a neighbor’s dog for one minute (60
seconds). Then you continue on to school traveling at 1 meter per
second (you had to speed up because you wasted time petting the dog).
It takes you a total of 15 minutes (900 seconds) to get to school, and
you travel a total of 1050 meters.
What’s your average speed?
Well, you just use the definition of average speed, which is
distance ball traveled
time to travel that distance
Putting in the correct numbers, you get
distance an object travels
time to travel that distance
=
1050 meter
1200 second
=
m
0.875
s
This can also be written as 0.875 m/s.
Of course, that average speed doesn’t give all the details of your
motion. If you tell someone your average speed, they have no idea how
fast you were traveling at any given time or whether or not you stopped
to pet a dog.
Average speed is easy to figure out. Just take the total distance
something travels and divide by the time it takes to travel that distance.
Instantaneous speed is not easy to figure out. You can’t just divide two
numbers. But the idea of instantaneous speed isn’t so difficult. It’s just
the speed you happen to be traveling at any particular time.
Adapted from Companion Classroom Activities for Stop Faking It: Force & Motion
Copyright © 2011 NSTA
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Oelfke (elf-ka)
Name:
Class:
Date:
Different Speeds
Answer the following questions as completely as possible.
1.
What does the speedometer on a car measure: average speed or instantaneous speed? How
do you know?
2.
Waldo gets stopped by the police, and the policewoman tells Waldo that she caught him on
radar doing 50 miles per hour in a 40-miles-per-hour zone. Waldo responds thusly: “No way I
was traveling 50 miles per hour. I sat at home for 1 hour and then drove for 1 hour before you
stopped me. I traveled 50 miles total in that second hour. So my speed was 25 miles per hour.
That’s well under the speed limit.”
Show how Waldo came up with a speed of 25 miles per hour. Then decide whether or not
Waldo should get a speeding ticket and explain why.
3.
Extra challenge: We haven’t discussed how to calculate instantaneous speeds. How do you
think you might go about doing that?
Adapted from Companion Classroom Activities for Stop Faking It: Force & Motion
Copyright © 2011 NSTA
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Name:
Class:
Date:
Evaluation
You are sitting by the side of a country road, and a car comes speeding along. Suddenly it stops in
front of you for just a second, then speeds off again in the same direction, going faster and faster as it
disappears from view.
Which of the following is true regarding the car’s motion?
1.
2.
3.
4.
Its instantaneous speed was never equal to zero.
Its average speed is the same as its instantaneous speed.
Its average speed during the motion was equal to zero.
Its average speed was never equal to zero.
Explain why you choose your answer.
Adapted from Companion Classroom Activities for Stop Faking It: Force & Motion
Copyright © 2011 NSTA
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