Force and Motion - Stamm/Wells/Long Teamand+Motion...Average speed is total distance divided by the total time needed to travel the distance. ... FOSS Force and Motion Course ... traveled

Force and Motion Name: _____________________________ Investigation 2: Speed Part 1: Who Got There First? If it is not possible to tell which vehicle arrived first at its final position, what additional information would we need to know in order to determine which vehicle arrived at 13 km or its final position first? Speed is the distance an object travels in a unit of time. The symbol for speed is a lowercase v. We use the words fast and slow to describe an object’s speed. If an object moves a long distance in a unit of time, we say it is going fast. If it moves a short distance in a unit of time, we say it is going slow. The units of speed are distance per unit time, such as kilometers per hour or meters per second. A fast car might travel at 150 km/h. A leisurely walker might travel at 1 m/s. An object’s speed is related to time. A time interval is how long it takes for something to happen. The amount of time it takes for an object to go a certain distance determines its speed. Lab Notebook, Who Got There First?, pages ___________ When two vehicles start together and go the same __________________ in the same

amount of ________________, they arrive at the final position together.

If vehicles go different _________________ in the same amount of ___________, the

one that goes farther is going faster.

If vehicles travel for __________________amount of _______________, you need to

find out how far they both go in 1 hour before you can compare them.

Green Resource Book, Time: The Infinite Line Part 2: Time Travel Review: You must know how long it took for a vehicle to travel the distance or how fast the vehicle was going. Lab Notebook, Time Travel A, page ____________ Try these: A car traveled 100 km in 2 hours. What was its speed?

A boy swam 75 meters in 3 minutes. What was his speed? A bicycle traveled 60 km in 4 hours. What was its speed? A girl walked 50 km in 10 hours. What was her speed? A bus traveled 369 km in 4.5 hours. What was its speed? Equation for calculating speed: v = symbol for speed d = symbol for distance traveled

v = _____d_____ Δt Lab Notebook, Time Travel B, page _________ Try these: A bus drove at 75 km/h. How far did it travel in 2 hours? A bird can fly at 8 m/s. How far can it travel in 10 seconds? A snail can creep along at 5 cm/min. How far can it travel in an hour? An arrow flying at 94 m/s struck the target in 1.8 s. How far away was the target? Lab Notebook: Speed, speed equation, distance equation Green Resource Book: First in Flight Part 3: Measuring Time and Distance Review: What two pieces of information do you need to know about an object in motion in order to determine its speed? What is the definition of speed?

What is the symbol for speed? What units are used to describe speed? What is the equation for calculating speed? If you know an object is traveling at a speed of 45 kilometers per hour, how can you determine how far it will go in 10 hours? Suppose you wanted to figure out how fast a bicycle was going. How would you go about it? In order to determine an object’s speed, we need to measure the distance the object moved, and we need to measure how long it took to move the distance. We know how to measure distance – we use a meter tape. How can we measure the time it takes for the object to move the distance? Practice using stopwatches You are going to figure out the speed of real cars rolling down slopes.

1. Find a good location for your ramp. Use a bit of tape to secure the downhill end of the ramp board to the surface.

2. Attach the smooth plastic surface on top of the board with a bit of tape. 3. Use books or other objects to elevate one end of the ramp. 4. Place a pillow wall at the downhill end of the ramp to stop the car safely.

Answer these questions: How long does it take your car to travel 200 centimeters down your ramp? What is your car’s average speed as it travels 200 cm down your ramp? Your elevated end or ramp should be exactly the height assigned.

A. Measure 200 cm from your xi to your xf . D= 200 cm Mark xf with a bit of tape. Place a jacket or sweater at the xf location. The car will come to a safe stop when it runs into the cushion.

B. Time several runs from the moment the car begins to roll until it hits the pillow wall.

C. Calculate the average time for a run. D. Calculate the car’s average speed as it travels 200 cm.

Lab Notebook, Speeding Down Slopes, page ________

Materials: 1 Ramp board 1 Plastic ramp surface 1 Dotcar 1 Meter tape Part F on Speeding Down Slopes: Did your car travel at the same speed during the whole run? How fast was it going at the beginning? How fast was it going in the middle of the run? At the end of the run just before it hit the pillow wall? It is difficult to know how fast an object is going at any specific time. Like our Dotcars, many moving objects change speed all the time. Their speed is not constant. To get around this problem, we often use an object’s average speed to determine how fast it is going. If we know how far something we went, and how long it took, we can calculate the object’s average speed. Average speed is total distance divided by the total time needed to travel the distance. In the example the car went 200 cm in 2.6 s. The total distance was 200 cm and the time (average) needed to travel the distance was 2.6 s. Dividing 200 cm by 2.6 s yields an average speed of 77 cm/s. What we are saying, in effect, is that if the car had been going at a constant speed of 77 cm/s for 2.6 seconds, it would have traveled 200 cm. Lab Notebook – Record definition: Average Speed Graph the Results Think About: Which Dotcar traveled fastest? Which Dotcar traveled slowest? What is the relationship between elevation and speed? Which Dotcar graph line has the steepest slope (goes up the steepest angle)? Which Dotcar graph line has the flattest slope? On a speed graph (distance versus time), what does the slope of a graph line tell you about the speed of the object?

Green Resource Book, How Fast Do Things Go? Lab Notebook, Average Speed Practice, pages ___________ Which Dotcar traveled fastest? Which Dotcar traveled slowest? What is the relationship between elevation and speed? Which Dotcar graph line has the steepest slope (goes up the steepest angle)? Which Dotcar graph line has the flattest slope? On a speed graph (distance versus time), what does the slope of a graph line tell you about the speed of the object? Green Resource Book, How Fast Do Things Go? Lab Notebook, Average Speed Practice, pages ___________

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FOSS Force and Motion Course© The Regents of the University of CaliforniaCan be duplicated for classroom or workshop use.

Lookatrace1betweenthetruckandcar.Neitherofthevehicleschangedspeedduringtherace.Whichvehiclereachedthe150-kilometer mark first?

Race 1

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Truckd= Trucktimeinterval= Card= Cartimeinterval=

Which vehicle reached the 150-km mark first?

How do you know?

Who goT There firsT? (race 1)

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Investigation 2: SpeedStudent Sheet

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Race 2



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Race 3

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a. How far did each vehicle travel?

Truck

Car

b. Howlongdidittakethevehicles togettotheirpositionsatxf?

c. Howfastwaseachvehiclegoing fromxitoxf?

d. Whatistheequationfor calculating speed?e. Whichvehiclegottothe 100-km mark first? How do you know?

Time Travel a

1. At2:30p.m.acarandatruckwereinthepositionsshownatxi.At3:30p.m.thecarandtruckwereinthepositionsshownatxf.Theytraveledatsteadyspeedallthetime.

Showmathandunitsintheseboxes.

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 240210 220 230

xi xf12

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a. Wherewouldthetruck be at 3:30 p.m.?b. Howfarwouldthetruck have traveled at 9:30 p.m.?c. Howfarwouldthecar have traveled at 3:00 p.m.?

Time Travel b

2. Thistimethevehiclesstartedatthepositionsshownatxi,butthetruckwasgoing half as fastasitwasinproblem1.

Showmathandunitsintheseboxes.

d. Whatistheequationforcalculating distance when you know the speed and time? e. Whatisthetotaldistancetraveled

byboth vehicles(addedtogether) at 5:00 p.m.?

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speed and disTance pracTice a

1. Bonnierodeherskateboard200meters(m)in30seconds(s).Raulrodehisunicycle300 m in 50 s. Who traveled faster? How much faster?

2. Itisabout384,750kilometers(km)fromEarthtotheMoon.IttooktheApolloastronauts about 2 days and 19.5 hours to fly to the Moon. How fast did they travel?

3. Achipmunkcanrun5m/s.Afoxcanrun8m/s.Ifthechipmunkandfoxstartrunning at the same time, will the chipmunk make it to its burrow in time?

4. Rita flew from Los Angeles to Boston to visit her aunt, a distance of 4000 km. The trip took 5 hours (h). What was the average speed of the jet?

5. Atruckleftadinerat1:00p.m.anddrove360kmtoJerseyCity.Thetruckarrivedat7:00p.m.Acarleftthesamedinerat2:00p.m.anddrovetoJerseyCityatanaveragespeedof80km/h.a. How fast did the truck travel?

b. Which vehicle got to Jersey City first?

6. An Arctic tern can fly 85 km/h for 24 h straight. How far can it fly before landing?

7. Rositastartedridingherbike3kmtoherfriendGena’splaceatexactlythesametimeGenastartedskatingtoRosita’shouse.Gena,ofcourse,wasn’thome,soRositarodebackhome.ThetwogirlsarrivedatRosita’shouseatthesametime.IttookRosita30 minutes to ride to Gena’s and back. How fast did Gena skate?

Rosita’s Gena’s

3km

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8. Ahikerwantedtohiketoalake26kmfromtheendoftheroad.Shestartedat6a.m.andwalkedsteadilyuntil9:00a.m.Shestoppedfora1-hourrestandthencontinueduntilshestoppedfor1.5htohavelunch.Shetookonlyone0.5hrestintheafternoonandarrivedatthelakeat7:00p.m.

a. What was the hiker’s average speed from the end of the road to the lake?

b. What was the hiker’s average speed during the time she was actually hiking?

9. Ronput16gallons(gal.)ofgasinhistruckandresetthetripodometerto0.Hedroveuntilheranoutofgas.Theodometerread480km.Howmanykilometerspergallondoes Ron’s truck get?

10. Beth’s motor scooter gets 110 km/gal. How far can she go on 2.5 gal. of fuel?

11.Achampionjumpingfrogcanjump2.5mevery4s.Whatisthejumpingfrog’saveragespeed?

12. An ostrich can run 10 km in 15 minutes. What is its speed in kilometers/hour?

13.Abasketballrolled300mdownahillin25s.Whatwasitsaveragespeeddownthehill?

14.AcommutergotonthetrainattheOakdaleStationat6:50a.m.ShegotoffatMetroStation at 8:05 a.m. The train made five 3-minute stops along the way. Oakdale is 21kmfromtheendoftheline,andMetroStationis96kmfromtheendoftheline.

a. What was the commuter’s average speed getting to work?

b. What was the average speed of the train while it was under way?

End of

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speed and disTance pracTice b


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response sheeT—speed

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Abbilookedattherepresentationoftheroadtripshownaboveandsaid,

I know how far the car went and how long it took to get there, but I’m not sure how fast it went.Gwensaid,

Here, I’ll show you how to figure out how fast the car was going.

1. What do you think Gwen showed Abbi?

2. Show Abbi and Gwen how to figure out how far the car had gone after 2.5 hours.


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speeding doWn slopesPart 1:Gatherdata.a. Theelevationyourteamworkedwithwas .

b. Thedistanceyouranyourcarwas .

c. Youran trials.

d. Enteryourrawdata.

e. Calculatetheaverage timeittookthecartotravel200cm.Useacalculator.

f. Calculatethecar’saverage speed. Writetheequationandshowyourmath.

200cm

Time trials(s)

Average speed

Average time

Part 2:Graphresults.a. Copytheotherteams’timeandelevationdata

toyourtable.

b. Graphdistanceversustimeforeachelevation.

200

200200

200200

Elevation Average d (cm) ∆t (s) (cm)


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1. WhenBelindawalkstoschoolinthemorning,ittakesher12minutestowalkthe1kilometer(km).Whenshewalkshomeafterschoolwithherlittlesister,ittakestwiceas long. Does Belinda’s speed increase or decrease when she walks with her sister?

2. Frank’scarrolled300centimeters(cm)in1.5seconds(s).

Noah’scarrolled360cmin2s.

Whose car ran on a steeper ramp?

3. Abikerrodeupa20-kmhillin2hoursanddownthehillin0.5hourwithoutstopping.Whatwashisaveragespeed

a. going up the hill?

b. going down the hill?

c. for the whole trip?

4. IttookEllie4hourstopaddlehercanoe10kmupstream.Afteraleisurely3-hourpicnic,shepaddledbackhomein1hour.

a. How fast did Ellie paddle upstream?

b. What was Ellie’s average speed while she was paddling her canoe?

5. Mark’sfamilydrove180kmtothebeachat90km/h.Theydrovehomeat60km/h.What was their average driving speed for the time they were on the road?

6. Threegirlsracedtheirmodelcarsdowna40-metertrack.Theirtimesareinthetable.Whatwastheaveragespeedatwhichthecars rolled down the track?

average speed pracTice a

7. Bentookoffinaplaneat9:30a.m.fromSeattleandlandedinBaltimore,4030kmaway,at7:00p.m.Therewasa1.5-hourlayoverinDenver.(ThetimeinBaltimoreis3hourslaterthaninSeattle.)

a. What was Ben’s average speed on his trip from Seattle to Baltimore?

b. What was the plane’s average speed while in the air?

Jessica 10 40

Kristi 20 40

Laticia 8 40

∆t (s) d (m)


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average speed pracTice b

8. Ahighschoolvarsityhardballpitchercanthrowhisfastball28.5min0.75s.Ahighschoolvarsitysoftballpitchercanthrowherfastball12.0min0.3s.Whichpitcher’sballtravels faster?

9. Aboatsailedouttoanislandataspeedof18km/hin4handthenimmediatelysailedback to port at 36 km/h in 2 h. What was its average speed for the trip?

10.Swetaenteredaskate,row,andbikerace.Hertimeanddistanceforeachlegoftheraceareenteredinthechart.

a. WhatwasSweta’saveragespeed for each leg?

b. Whatwasheraveragespeedover the whole race?

Skate 1.25 20

Row 0.75 6

Bike 2.5 100

∆t (h) d (km) v (km/h)

11. Biff’s dog loves to catch his tennis ball. It takes the ball 5 s to fly 60 m.

a. How fast does Biff’s dog have to run to catch it?

b How fast is that in kilometers per hour?

12.Lily’sfamilytookamotorboat24kmdownariverforapicnic.Ittookthem1htogettothepicnicspot.Theridebacktothedocktookanhourandahalf.

a. What was the boat’s average speed going to the picnic?

b. What was the boat’s average speed coming home from the picnic?

c. What was the boat’s average speed for the whole boat ride to and from the picnic?

d. What was the average speed at which the river flowed?

e. What would the boat’s average speed be on a lake?

13. What is the average speed of an arrow that takes 1.25 s to hit a target 75 m away?


Documents

Force and Motion - Stamm/Wells/Long Teamand+Motion...Average speed is total distance divided by the total time needed to travel the distance. ... FOSS Force and Motion Course ... traveled