ID:
NAME:
Velocity POGIL #1 (When you see a
DATE:
CLASS:
, check in w/teacher!)
Warm Up:
1. What does this symbol mean?
2. What does this symbol mean?
3. What does this symbol mean?
4. What does this symbol mean?
5. What do these symbols mean?
6. What does this symbol mean?
$
7. Can symbols be used to express an idea or concept? (yes/no) Explain:
8. What does this arrow mean?
9. What does this arrow mean? Compare/contrast it to the arrow in #7:
10. What is the difference(s) between the arrow in #7 and this arrow?
11. What two properties of arrows seem to be illustrated by 7, 8, and 9?Explain:
12. Could an arrow indicate which way something moves?
13. Could an arrow indicate how fast something moves?
14. Summary: Can an arrow describe the size and direction of a physical quantity?
Idea for the Warm Up modified from: http://ed.fnal.gov/arise/guides/phys01-vectors.pdf
Distance and displacement are two quantities that may seem to mean the same thing yet have distinctly different
definitions and meanings.
 Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
 Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall
change in position.
To test your understanding of this distinction, consider the motion depicted in the diagram below. A physics teacher
walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

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


Even though the physics teacher has walked a total distance of 12 meters, her displacement is 0 meters.
During the course of her motion, she has "covered 12 meters of ground" (distance = 12 m).
Yet when she is finished walking, she is not "out of place"
o i.e., there is no displacement for her motion, or CHANGE in her position (displacement = 0 m).
Displacement, being a vector quantity, must give attention to direction.
o The 4 meters east cancels the 4 meters west;
o and the 2 meters southcancels the 2 meters north.
Vector quantities such as displacement are direction aware.
Scalar quantities such as distance are ignorant of direction.
In determining the overall distance traveled by the physics teachers, the various directions of motion can be
ignored.
1. Now consider another example. The diagram below shows the position of a cross-country skier at various
times. At each of the indicated times, the skier turns around and reverses the direction of travel. In other
words, the skier moves from A to B to C to D.
a.
Using the above diagram in which the skier moves from A to B to C to D.
What was the skiers DISTANCE traveled?________________________
b.
What was the skier’s resulting DISPLACEMENT?_________________
2. Consider a football coach pacing back and forth along the sidelines. The diagram below shows several of
coach's positions at various times. At each marked position, the coach makes a "U-turn" and moves in the
opposite direction. In other words, the coach moves from position A to B to C to D.
a.
What is the coach's resulting displacement?__________________________
b.
What is the coach's distance of travel? ________________________________
CHECK YOUR UNDERSTANDING:
3. What is the displacement of the cross-country team if they begin at the school, run 10 miles and finish back at the
school? EXPLAIN:
4. The Indy 500 is a 500 mile race.
a.
b.
c.
What the distance of the race car drivers in the Indy 500?__________________________________
What the displacement of the race car drivers in the Indy 500?____________________________
EXPLAIN:
Formula In Words
Velocity is…
 How fast something goes in a specified direction
 DISPLACEMENT divided by time interval
HOW TO WRITE THIS FORMULA
Δ d = d2 – d1
v = Δt
Δt
v indicates velocity
Δ d indicates DISPLACEMENT, or the CHANGE IN position
d2 indicates FINAL POSITION
d1 indicates INITIAL POSITION
5. A car travels 60 km north, turns around, then travels 60 km south. The entire trip takes 2 hours. What was its
average speed? SHOW WORK or EXPLAIN:
6. A car travels 60 km north, turns around, then travels 60 km south. The entire trip takes 2 hours. What was its
average VELOCITY? SHOW WORK or EXPLAIN:
Please complete the following problems using all the steps we practiced last class:
7. The slowest animal ever discovered was a crab found in the Red Sea. It traveled with an average speed
of 5.70 km/year. How many years would it take this crab to travel 100 km?
Known Variables:
Unknown Variables:
Show Your Work in This Box:
Write Your Final Answer Here…include units!!!
Formula
8. On May 28, 2000, Joe Montoya became the first Columbian citizen to win the Indianapolis 500.
Montoya completed the race in a time of 2.98 hours. What was Montoya’s average speed (IN BOTH miles
per hour AND kilometers per hour) in the 500 mile race?
Known Variables:
Unknown Variables:
Formula
Show Your Work in This Box:
Part A (answer in miles per hour):
Part B: (answer in km/h):
Part B: what was Montoya’s average velocity? Justify WHY you answered the way you did:
_______________________________________________________________________________________________________________________________________
_______________________________________________________________________________________________________________________________________
9.
You watch a thunderstorm from your living room window. You see a lightning bolt flash, and you
begin counting the seconds until you hear the thunder clap ten seconds later. Assume the average speed of
the sound in air is 340 m/s. How far away was the lightening bolt in meters, miles, and kilometers? (Note: the
speed of light is much faster than the speed of sound. This is why you see the lightening much earlier than you hear the
thunder. In reality, they actually occur almost simultaneously. More on this when we learn about Waves, Sound, and
Light!)
Known Variables:
Unknown Variables:
Formula
Show Your Work in This Box:
Part A (answer in meters):
Part B: (answer in miles):
Part C: (answer in km):
CHALLENGES: Complete these when you finish the previous questions!
10.
You stand at the top of the Grand Canyon and yodel down to the bottom. You hear your yodel ECHO
back from the canyon floor 5.2 seconds later. Assume that the average speed of sound in air is 340 m/s. How
DEEP is the canyon floor? (Hint: you may want to draw a picture for this. Think about what the question is asking!!)
Known Variables:
Unknown Variables:
Formula
Show Your Work in This Box:
Write Your Final Answer Here…include units!!!
11.
It is now exactly 7:29 am, but when the bell rings exactly one minute later at 7:30 am, you will be late
for Physics for the 3rd time!!! You MUST get from one side of RHS to the other by hurrying down 3 different
hallways in order to avoid a Friday detention. You run down the first hallway, a distance of 35 m, at an
average speed of 3.5 m/s. The second hallway is filled with students, and you cover its 48 m length at an
average speed of 1.2 m/s. The final hallway is empty, and you sprint down its 60 m length at an average speed
of 5 m/s. Do you make it to Physics on time, or do you earn a Friday detention?
Known Variables:
Unknown
Formula
Variables:
Show Your Work in This Box:
Write Your Final Answer Here
Additional Practice – solve on a separate sheet of paper and attach
1. Anne takes her dog for a walk. They walk 250 m [West] and then back 215 m [East] before stopping to
talk to a neighbor. Draw a vector diagram to find their resultant displacement at this point.
What was the total distance that Anne walked?
2. This time, Anne daughter takes the dog for a walk. They leave home and walk 250m [West] and
then back 175 m [East] before stopping to talk to a friend. What is the displacement at this point.
3. This time the dog walks himself. He heads 30m [W], stops, then goes farther 50m [W] before
returning 60m [E]. What is the resultant displacement? What is the total distance traveled?
4. An actor walks 5m stage right (east in this case) and the 15m stage left.
a. Find the displacement by drawing a vector diagram.
b. What is the total distance traveled by the actor?
5. A shopper walks 35m [W], another 17m [W], and then 67m [E]. Show the problem by drawing a
vector and finding the displacement.
6. On a paper delivery route, Julia walks from home three blocks north to collect her newspapers,
walks back eight blocks south while delivering the papers, and then returns home. State Julia’s
displacement and direction.
7. A train travels at a constant speed through the countryside and has a displacement of 150km [E]
in a time of 1.7h. What is the velocity of the train?
8. Monarch butterflies migrate from Eastern Canada to central Mexico, a resultant displacement of
about 3500km [SW] in about a time of 2184 hours. What is the average velocity of the monarch
butterflies in kilometers per hour (km/h)?
9. A Monarch butterfly usually flies during the day and rests at night on its migration. If a particular
butterfly Is travelling at an average velocity of 19km/h [S] for 230km [S] on one part of its
journey to Mexico, how long does this take?
10. While delivering fliers, Brad walks 1.00km [N], 0.50km [E], 1.00km [S] and finally 0.50km [W] in a
total time of 1.5h.
a. What is the total distance travelled?
b. What is Brad’s average speed?
c. What is the resultant displacement?
d. What is Brad’s average velocity?
Some information in this POGIL sourced from the following sites:
http://www.physicsclassroom.com/class/1dkin/u1l1c.cfm
http://bmuise.wikispaces.com/file/view/Adding+Vectors+and+Velocity+Worksheet.pdf