Physics NamePeriod Date

C-3 Vocabulary - Position, Speed and Velocity

1. Average speed17. dependent variable

2. Constant speed18. X-axis

3 Coordinates19 Y-axis

4. coordinate system0. at rest

5. displacement21. constant

6. instantaneous speed

7. origin

8. position

9. ra e

10. slope

11. time

12. vector

13. velocity

14. variables

15. data

16. independent variable

22. experimental variable

Physics NameChapter 3 Section Review Questions

Section 3.1

1. Where do you end up relative to your starting point if you walk 20 kilometers due east and then 35kilometers due west?

2. A weather balloon is 2 kilometers above the surface of Earth. As you watch it, the balloon floats15 kilometers west and 8 kilometers north of its starting point Write the balloon s location as aposition vector in the form (x, y, and z).

3. What distance is covered in 45 minutes if a bicycle rider s speed is a constant12 km/hour?

4. Why is speed always non-zero whereas velocity can be positive, negative, or zero?

Section 3.2

1. A com uter train travels at 60 km/h for 10 minutes and at 40 km/h for 30 minutes. What is thetrain’s average speed for the 40-minute time interval?

2. The slope of a distance-versus-time graph for a bicycle rider is zero for a 75-minute time intervalWhat is the bicycle rider s speed during that time interval? Explain.

3. A car travels 150 km for two hours east of a starting point, turns around and travels due west 300km for three hours What is the car s net velocity t r the trip?

4. A speed-versus-time graph for a falling pine cone shows a straight line from a time of zero and aspeed of zero to a time of 2 seconds at a speed 19 6 m/sa. What geometric figure is formed by the straight line and the speed and time axes?b. How far, to the nearest meter, does the pine cone fall in 2 seconds?

Section 3.3

1. \fd=vt,vt=d Is it also true that if v = d f, then fd = v? Explain.

2. Use the position-versus-time equation x = Xq + vtto determine how long it will take a model carmoving at -3 cm/s to reac the point = 0 if its starting position is at0 = 42 cm.

3. The position-versus-time equation x = x0 + vt can be rewritten as v = (x - x0)/f. Ifx = 5 km and x0 = 15 km, why does v have to be less than zero?

©CPO Science

Distance and Displacement Worksheet Name:For each question plot the path on the grid paper.

1. oey drives his Skidoo 7 kilometres north. He stops for lunch and then drives 5 kilometres east.W at distance did he cover? What was his displacement?

2. A thony walks to the pizza place for lunch. He walk 1 km east, then 1 km south and then 1 kmeast again. What distance did he cover? What was his displacement?

3. On his fishing trip ustin takes the boat 12 km south. The fish aren t biting so he goes 4 kmwest. He follows a school of fish 1 km north. What ist nce did he cover? What was hisdisplacement?

4. Preston goes on a camel safari in Africa. They he travels 5 km north, then 3 km east and then 1km north again. What distance did he cover? What was his displacement?

5. Neil pogo sticks to his science class. He travels 8 m east the 4 m north. What distance did hecover? What was his displacement?

6. Ala rents a private jet for the weekend. He flies 400 km south to New York, then flies 700 kmwest to Chicago, then 1200 km south to Miami. What distance did he cover? What was hisdisplacement? (use 1cm = 100km)

7. Brandon buys a new Seadoo. He goes 12 km north from the beach. He jumps wakes for 6 kmto the east. Then chases a boat 10 km north. What distance did he cover? Whst was hisdisplacement?

8. Alex goes cruising on his dirt bike. He rides 700 m north, 300 m east, 400 m north, 600 mwest, 1200 m south 300 m east and finally 100 m north. What distance did he cover? Whatwas his displacement? (use 1cm = 100m)

9. Stephen buys a new moped. He travels 3 km south and then 4 km east. How far does he needto go to get back to where he started?

Physics Problems Name Period Date

Numerical Challenge Problems - work on your own or with a partner (but not a group of...)

Draw a sketch (labeled) of the situation and figure out a way to solve the problem.

1. An ambitious hiker walks 25 km west and then 35 km south in a day. Find the magnitude

and direction (relati e to due west) of the hiker's resultant displacement.

2. I went for a walk the other day. I went four a enues east (0.80 miles), then twenty-four

streets south (1.20 miles), then one avenue west (0 20 miles), and finally eight streets north

(0.40 miles).

a What distance did I travel?b. What's my resultant displacement?

3. in the fictitious city of Metropolis, streets run east-west while avenues run north-south. The

separation between centers for both the streets and the avenues is 100 m, resulting in

square city blocks. Superman is located at 33rd Street and 3rd Avenue while Lois Lane is

located north and east of Superman at 45th Street and 12th Avenue.

a. How far would Lois Lane have to walk to reach Superman?

b. How far would Superman have to fly to reach Lois Lane?

c. In what direction should Superman fly to reach Lois Lane as quickly as possible?

Physics Problems Name Period Date

Distance vs. Displacement Problems

Dis ance is a scalar value (direction does not mat er) Avg.Speed is distance/ time

Displacement is a vector value (direction matters) Velocity is displacement/ time

1. A mountain climbing expedition establishes a base camp and two intermediate camps, A

and B. Camp A is 11,200 m east of base camp. Camp B is 8,400 m west of Camp A. Make

a diagram that uses the base camp as the origin and shows the relative positions of both

camps. Using this information, determine the displacement between base camp and

Camp B.

2. The mountain climbers travel from the base camp to camp A and then to camp B at a very

steady pace of 2.7 km/hr.

a) What is their distance?

b) What is their displacement?

c) How long will it take to get to camp B?

d) What is their average velocity?

3. Ms. Martin arrives at school at 7:00am, walks from her car in the parking lot to her

classroom which is 525 steps south. She is immediately called to the office for a message

and walks 325 steps to the office northeast from her classroom. When she gets to the

office, the secretary realizes that she has called the wrong teacher and sends Ms Martin

back to her classroo . After her first class, Ms. Martin realizes that she has left her purse in

her car and dashes out to the parking to get it. Then races back to class just in time for 2nd

hour.

a) Since first hour started at 7:30, what was her avg. speed at the beginning of first hour?

a) What is her distance traveled at the beginning of 2nd hour?

b) What is her displacement at the beginning of 2nd hour?

4. If an unfortunate accident happens during third hour and Ms. Martin has to go back to the

office to find a left handed staple remover, and then co es back to class. What is her totai

distance travelled now? the displacement?

5. At the end of the day, Ms. Martin goes back to the office to return the LHSR, but the office is

locked, so she goes back to her room and packs up her papers. She trudges out to her car

at 5:00pm, only to discover that she forgot to shut the lights off and her battery is now dead.

She sits on the car and grades papers while she is waiting for a rescue.

a) What is the total distance she has travelled now?

b) What is her displacement?

c) what is her avg. speed (in steps/hr)?

d) What is her avg velocity?

6. According to answers,com. Earth travels approximately 940 million km in one year.

Calculate both the distance and the magnitude of the displacement of the earth after...

a. one complete orbit around the sun

b. one-half orbit around the sun

c. one-fourth orbit around the sun

d. What relationship between distance and displacement does this illustrate?

Conceptual review

1. For each of the following questions, decide whether the question is asking for the

or the magnitude of the displacement (or both or neither).

a. How far o you walk each day? Dist. Disp. Both

b How far is it from Toronto to Mexico City by airplane? Dist. Disp. Both

c. How far is it from Toronto to Mexico City by car? Dist. Disp. Both

d. How far is the earth from the moon? Dist. Disp. Both

e. How long is a standard sheet of plywood? Dist. Disp. Both

f. How long is the coastline of Britain? Dist. Disp Both

g- How long is the trac on a compact disc? Dist Disp. Both

h. How long did it take you to get here? Dist. Disp. Both

i. How many frequent flyer miles do you have? Dist. Disp. Both

i- What is the radius of the earth? Dist Disp. Both

distance

neitherneither

neither

neither

neitherneither

neither

neither

neither

neither

Name:

Period: Graphing Speed; Slope

The graph on the right is adistance versus time graph.

That means that it shows how faran object has traveled after so

many seconds.

This is what we call alinear raph, because the data

creates a str ight line.

Time Distance(sec) (m)

0 00.5 5

1 101.5 152 20

Slope has actual meaning in science - slope for the above graph:

rise Ay y2-yi (20-10)m 10mslope = = = = = = lOm/s

run x x2-xi (2 - 1) sec 1 sec

The slope of a

position vs. ti e graph

i SPEED

Graphin Conventions: The independent variable is always on the x-axis.The dependent variable is al ays on the y-axis.

2.5-

Point(2,2)

\Position vs. Time Point 2

(10,2)

/?oS iw 1

£ OG

S .2 n --o -O ua ca

Q > Time (sec) l*1

1dependervariable

0 12

t

Independent variable TimeDependent variable position

Linear gra h.

Position vs. time aph, soslope = speed (position/time)

(Pick any two points)Slope = rise/run = Ay/Ax =

(2 - 2)m 0 m0 m/s

(10-2) sec 8 sec

Time is al aysan independent

va iable (x-axis).

The slope (speed)of a flat line is

zero no speed.

The object is at rest.

Steep slope fast speed

¦ - - »

Gradual slopeslow speed

slope =Ay (35 - 5)m 30mAx (5 - 0)sec Ssec

6m/s ) slope =Ay (15-5)m 10mAx (10-0)sec lOsec

1. Lineal-

2. Independent variable

3. Dependent variable

4. Slope

The variable on the vertical axis (y-axis).

A type of graph that looks like a straightline.

The measure of the steepness of a line.

The variable on the horizontal axis (x-axis).

Which of the following are units for speed?

km meters meters cmsec sec

sec miles km meterhour min sec2

Which is the independent variable?

Which is the dependent variable?

Where was the object at 4 seconds?

Find the slope of the graph ( ust show work)

What does the slope you just found stand for?

350Distance vs.Tme

1

5

Time (sc;cs)10 11

When did the object reach 150 meters?

Where was the object at 9 seconds?

Find the slope of the graph (must show work)

What does the slope you just found stand for?

Which is the independent variable?

Which is the dependent variable?

Where was the object at 4 seconds?

Find the slope of the gr ph (must show work)

What does the slope you just found stand for?

The slope of this graphmeans:

The segment that showsfa t speed:

The segment that showsslow speed:

Position vs. Time

Time Time

Which graph segmentsfit the following:

At rest:

Fast speed:

Slow speed:

Going backwards:

Going forward:

Name:

Period: Speed and Experiments

Speed

Speed is how fast something isgoing. Precisely, it is the

amount of distance t aveled in acertain amount of time.The standard units are

meters per second, but any unitsof distance/time will work.

Speed(in meter/sec)

Change of Distance(in meters)

Change of Time(in seconds)

Speed equal change of distancedivided by change of time.

AD = D, D AT = T? I,

A ca 4 meters away fo 2 hours has a speed of zero it hasn t moved. That s why

we have to use AD/ATinstead of D/T the objec

has to be moving.

A plane flies 4000 miles in 5 hours. A car travels from 20 meters to 60 meters A car travels at 60 m/s for 8 seconds.Calculate the plane’s speed. in 10 seconds. Calculate the car’s speed. Calculate the distance it travels.

Step 1: variables Step 3: Solve for unknown Step 1: variables Step 3: solve for unknown Step 1: Step 3:S = ? variable: variable:

AD = 4000 miles Already done: S = AD/ATAT = 5 hours

Step 4: Put in nu bersStep 4:

Step 4:Step 2: for ula S = 4000 mi/5 hr Step 2: formula

Step 5:Step 2:

Step 5:S = AD/AT Step 5: Calculate answer

The Scientific Method:

Really R ResearchQuiet Q Question

Hippos H HypothesisEat E Expe iment '

Dark D DataChocolate C Conclusions

Experi ents

Experiments are how we gaindata (evidence) to prove ordisprove a hypothesis.

If experiments are goinglead us to nowledge, webetter know how to dothe correctly so that ourdata eally is proof!

Trials A trial is one time an experiment is run. Data ho experiments are often recorded in data tables.

Good experiments have several trials.Why? Because to really proof some¬thing, and experiment must be repeatableby others. One ti e through an experi¬ment proves nothing there might havebeen a mistake, for instance.

A Data Table

Trial Time (sec)1 2.5

2 33 3.1

4 2.8

5 2.9

Ave Time 2.86

Usually, data changesa bit with each trial.Which one is best?

An average is better thanan individual trial’s data.

VariablesA variable is a part of anexperiment that can change.

Procedures

In most experimen s thereare many variables. Whentalking about speed we onlyneed two: distance and time.

Your procedure is how youperform an experiment.

Good data requires oodexperimental procedures.Spending time developing oodprocedures ensures your d tawill be accurate and your con¬clusion believable.

Your procedure is alist of how you didyour experiment.

1

Name.

Period

I Variable A. How an expenment is actually conducted. Match the variables on the left with the quantities on t e right

B. A part of an experiment that can be 1. a = 50 m/s2changed or manipulated.

2. S or v - 103. Data Table C. A setup used to gather data and know - 3 m - 20 meters/sec

edge.

4. Trial 4. D = 228 metersD One time an ex eriment is run.

5. F = 15 kgm/s5. Expenment E. A list of information fiom an experiment.

6. p = 78 sec

Fill in the math functions 7. T = 6 newtons

SAT- S AT D - Di D D, 8 E = 12 joules

9 MA = 36 kilogramsS/T = S T a/AT = a AT

F = ma S AD/AT AD = D2-D| a = AS/ATSolve for a Solve for AD Solve for D2 Solve for AT

A bike moves 50 m in 5 seconds.Calculate the speed of the bike.

A car travels 200 miles m 8 hours.Calculate the car s speed.

Step T vanables-S =AD =AT ==

Step 2: Formula:

Step 3: Solve for the unknown variable'

Step 4- Plug in number.

Step 5 C lculate an answer-

Step 1. Step 3.

Step 2

Step 4.

Step 5:

A car travels 60 m/s for 60 secs.Calculate how far it tiaveled.

On holiday, a family travels from Meyerville (10 miles away) toSprytown (50 miles way), m 3 hours.

Calculate the family’s speed.

Sten 1: Step 3: Step 1 Step 3:

Step 2:

Step 4:

Step 2:

Step 4

Step 5: Step 5-

AHS Physics NameDate Period

Displacement and Velocity WorksheetShow all work as you solve the following problems.

1. Calculate the total displacement of a mouse walking along a ruler, if it begins at thelocation x = 5cm, and then does the following:

- It walks to x= 12cm- It then walks a displacement of -8cm- Lastly, it walks to the location x = 7cm

2. Find the average elocity (in m/s) of a bicycler that starts 150 meters north of townand is 1200 meters north of town after 30.0 minutes

3. Explain what is wrong with the following statement1 A man walked at an averagevelocity of 5.2m/s

4. A school bus ta es 0.53 hours to reach the school from your house If the averagespeed of the us is 19km/h, what is the displacement of the bus during the trip?

5. A girl participating in cross-country spends the afternoon practicing, and ends thepractice completely tired from her hard work, despite the fact that her averagevelocity during the practice was O.Om/s. Explain how this situation is possible.

6. A hiker is at the bottom of a canyon facing the canyon wall closest to her. She is280.5 meters from the wall and the sound of her voice travels at 340 m/s at thatlocation. How long after she shouts will she hear her echo? (Be careful to considerwhy echoes happen)

Questions #7-12 all have to do with position-time graphs of different riders in abicycle race. Match each graph with the explanation that makes the most sense,

and write the letter of the explanation next to the appropriate number. (Someexplanations will not be used.)

A. slow, constant rate E.

B. started late F.

C. went back to take a picture G.

D. spectator standing still H.

fast constant rategradually increasing speedgradually decreasing speedleg cramp causes sudden drop in speed

13. An object moves at a slow, constant vspeed, then sits at rest for a moment, athen moves at a new faster, constantspeed. Sketch a velocity-time graph ofthis motion on the gi en axes.

t(s)

14. The following data was taken during a student s experiment with an object movingat a relatively constant velocity Use the data to create a position-time graph (onthe accompanying graph paper). Be sure to include a best-fit line. After the graphis completed, use your best-fit line to calculate the average speed of the object.Show speed calculations below.

Time (s) Position (cm)0 0 001 0 802 4 16036 24 549 31 56.2 40 0

Name.Period

Constant Velocity WorksheetDate

Consider the position vs. time graph below for cyclists A and B

a. Do the cyclists start at the same point How do you know? If not, whichahead?

b. At t = 7 s, which cyclist is ahead? How do you know?

c Which cyclist is traveling faster at 3 s? How do you know?

d. Are their velocities equal at any time? How do you know?

e What is happening at the intersection of lines A and B?

Constant Velocity Worksheet 1

2

a.

Consider the position vs time graph below for cyclists A and B

How does the motion of the cyclist A in this graph compare to that of A in theprevious graph on page one?

b. How does the motion of cyclist B in this graph compare to that of B in theprevious graph on page one?

c. Which cyclist has the greater speed? How do you know?

d. Describe what is happening at the intersection of lines A and B.

e. Which cyclist has traveled further during the first 5 seconds? How do youknow?

Name Period Date

Constant VelocityWorksheet 2: xvs.t and vvs. graphs

Sketch the position vs time and the velocity vs time graphs corresponding to thefollowing descriptions of the motion of an object

X V1. The object is moving away

from the origin at a constant(steady) speed.

-t t

x2. The object is standing still.

v

t

X V3 The object moves toward the

origin at a steady speed for10s, then stands still for 10s

+>t

X V4. The object moves away from

the origin at a steady speed for10s, reverses direction andmoves back toward the originat the same speed

Constant Velocity Worksheet 2: VS. 2" and V VS. graphs

Draw the velocity vs. time graphs for an object whose motion produced theposition vs. time graphs shown below at left.

7.

fa+2

* :

- " • I

E;

S 0: o :» -1;

* * t * A1

* * f * * t A2 3

lii

4 Tlmejts)

physics.info

GRAPHS OF MOTION COMPARED

displacement-time velocity-time acceleration-time

intercept

slope of tangent

positive slope

negative slope

zero slope

straight

curved

area under curve

curves coincide

stopped when...

uniform acceleration

j

Physics Name Challenge Problems - Velocity Date Hr

Challenge Probiems - Velocity

Solve each of the following problems...be sure to include ALL of the steps'

1. A man is at sea on a raft, adrift on the ocean current. The current carries him 51 miles in 3 days. At thisspeed, how long would it take him to travel 400 miles

2, A man competing in a bicycle race travels 57 km in 3.0 hours. If he aintains this average spee , how farwill he go in 8.0 hours?

3. Your dog is sent to fetch the newspaper in t e morning. He runs directly away fro you, tra eling 62.0feet in 5.0 seconds. He t en turns aroun and in 4.0 seconds runs 30.0 feet back toward you before decidingto stop. Calculates the dog s average speed and average velocity.

4. Two cars are 12 miles apart and are approaching each other on a straight road. Each car is moving at 60mi/h relative to the road. How long will it be before the cars pass eac other? Give your answer in inutes.

5. A car travels at a speed of 30 km/h for a distance of 12 . It then reaches a freeway here it travels at85 km/h for 40 k . Find the average speed of the car for the en ire trip.

PhysicsSG Ch. 3

Name Date Hr

Study Guide Ch. 3 Displacement Speed Velocity & Position Time GraphsI. Displacement

1. What is the definition of distance?2. What unit of measurement do we use to express distance?3. Is distance a scalar or vector? How do you know?4. What is displacement?5. Is it a scalar or vector?6. 20 m south; is this a vector or scalar?7. If you walked 4 m south, 6 m north and 2 m south: what is the distance you walked?8. What is the displacement that you walked?9. What is the equation that we use for displacement?10. In the value -20m south; what would be the magnitude?11. What does the negative value mean?12. Would this be referring to the distance or displacement?

II. Velocity1. What is the different between speed and velocity (how are they the same, how are they different?2. The airplane is moving 300 mi/hr...is this its speed or velocity?3. The airplane is moving 300 mi/hr, west...is this speed or velocity?4. Is speed a vector or scalar?5. Is velocity a vector or scalar?6. What is the formula (detailed) for velocity?7. If your position NEVER changes, what is your displacement?8. If your displacement is zero, what is your velocity?9. When would you have a positive velocity?10. When would you have a negative velocity?11. You observe a squirrel running 105 meters North in 5.5 seconds, what is its velocity?12. If you bike at a velocity of 17 miles per hour, how many seconds will it take her to cover a 98 mile course?13. If the bus stop is 0.98 km down the street from the museum and it takes you 11.98 min to walk north from thebus stop to the museum entrance, what is your average velocity?14. What is the shortest possible time that a Volvox globator cou\d move across a microscope slide with a diameterof 7.98 cm at a velocity of 3.5 mm/s north?15. A drop of blood travels at a velocity of 20 mm/s, how far did the blood travel in 2 sec?16. Convert 20s into hours.17. Convert 20 mi/hr to m/s.

III. Position Time Graphs1. What is the most important thing to know about a graph?2. What is the formula for slope?3. On a position time graph, what axis would you put the position on?4. What axis would you put the time on?5. When reading a position time graph what does the slope mean?6. What are the 2 types of velocity?7. When reading the following; what is the velocity between 1 s and 10 s , would this be asking for the averagevelocity or the instantaneous velocity?8. When reading the following; what is the velocity at 1 s , would this be asking for the average velocity or theinstantaneous velocity?

TABLE 1: Position Time Graph For Arrow in Flight

Position (meters) Time (sec)

0.0 0.030.62 0.559.06 1.085.30 1.5

109.73 2.0132.69 2.5154.20 3.0174.25 3.5193.57 4.0

1. What is the arrow s position of the object at 2.5 seconds?

2. What is the displacement of the object between 1.5 sec and 4.0 seconds?

3. What is the average velocity of the object between 1.5 sec and 4.0 seconds?

4. What is the average velocity of the entire trip of the object?

Poston (mstere) Poston !jrr» )

5. An object at rest 6. An object with a constantpos tive velocity

7. An object with a constantnegative velocity

p p P

0 0 0

s s s

Time Time

Tim (seconds)

8 What is the total distance the object tra eled?

9. What is the displacement of the object between 1.6s and 5s?

10. Is the velocity increasing or decreasing?

11. Is the velocity positive or negative?

12. What is the average velocity of the object between 2s and 4s?

13. What is the instantaneous velocity of the object at 3s.

14. Is the velocity increasing or decreasing?

15. Is the velocity positive or negative?

16. What is the average velocity of the object between ,4s and 3s?

17. hat is the instantaneous elocit of the object at 2s.

Time (seconds)