Section 11.2 Speed and Velocity

Transcription

1 / Name Class Date Section 11.2 Speed and Velocity This sectian defines and comparcspeed and uelocity. It also describes how to calculate aatrage speed. Reading Strategy Monitoring Your undelstanding After you read this section, identify several things you have learned that are relevant to your life. Expiain yhy they are relevantto you. For more information on this Reading Strategy, see the Reading and Study Skills in the Skills and Reference Handbook at the end of your textbook. What ls lmportant Facte About Speed and Vetocity tthy lt ls lmportant Speed, - ' 1. Define speed. 2. The SI units for speed are 3' How is instantaneous speed different from average speed? 4. The equation used for calculating average speed is 5. Is the following sentence true or false? you can determine how fast you were grohs the. 1t midpoint - speed for the entire of trip. a trip by calculating average 5. A sfudent walked 1.5 km in 2s minutes, and thery realizing he was late, ran the remaining-o.skm in 5 minutes. Calculate hi, ururug* speed on the way to sdrool. 7' what type of speed does an automobile's speedometer display? Graphing Motion, 8. The slope of a line on a djstance-time graph represents

2 Name Class Date For questions 9 through 11, refu to tlw graphbelow. o iert.4#t:... :... :...: Draw a point on the graph that represents 200 m traveled in 4 seconds. Draw a line connecting this point with the origin (0,0). Label this as line A. 10. Draw a point on the graph that represents 100 m traveled in L0 seconds. Draw a line connecting this point with the origin (0,0). Label this as line B. 11. calculate the average speed (slope) of lines A and B. Be sure to include units. Velocitlr:,,\. l 12. How do speed and velocity differ? 13. Circle the letter of each sentence that describes a change in velocity. a" Amoving object gains speed. b. A moving object changes direction. 'I c. A moving object moves in a straight line at a constant speed. d. A moving object slows down. 14. Is the following sentence true or false? If a car travels around a genfle curve on a highway at 50 km/h, the velocity does not change. Gombining Velocities 15. How do velocities combine? 15. A river flows at a velocity of 3 km/h relative to the riverbank. A p^o_at mov.es upstream at i velocity of t5 k*/h relative to the Itvhat river. is the verocity of the boat relative to the riverbank? a. 18 km/h downstream b. 15 km/h upstream c.12km/hupstream d,. 12 krrr / h downstream :-,::l {

3 t5 Name Class Date Section 11.2 Speed and Velocity 1g:Ags* &L- : -'l'o Yo Gontent and Voeabulary Support C a l cu l ati ng Ave rage Speed Speed Speed ig a measure of how fast somethirrg is moving. It is calculated by dividing the distance an object moveli by the amount of time it takes the object to move that distance. For example, a car that travels 50 kilometers in one hour has a speed of 50 km/h. Irr other words, speed is a ratio of distance to fime. V1"y objects do not rnove at a constant speed. For example, a car traveling at a speed of 50 km/h may slow clown as it approaches a red light and then speed up again when the light turnfgreen. The car's speed at any given moment in time is calied its instantaneou8 speed. Avenge Speed Although an object may not have a constant speed, its motion over a gilen distance can be expressed as its averagespeerr. Average epeed is the total dietance traveled, divided by the-totii time it takes td travel that distance. The equation for average speed is: Average speed : ffi, oro:4 For example, if a car travels B0 kilometers in the first hour of a twohour: trip and 100 kilometers in the seconcl hour; its average speed for the total trip would be: - * -(80 km * 0 : --T1 T[t*) : f8o *ifi km _ h +ft)-- : 9o km/hr The equation for averag speed can tre rewritten to find either the total time or the total distance when the other two.i,ariables are known: ) t:#andd:dxf e 1,,., l-;-i -,3 \.r1-.*lq'1x.y11l

4 rf Name Class Date Snction I Le $peed and Velocity $olved Examples Example 1: Awinner of the Indianapols 500 autn race completed the kilometer race in 2.98 hours. What was the driver's average speed dururg the race? Giam: Total distance (d) : km Total time (f) : 2.98 h Unkttoum: Average speed (O) ' : : Equation: E: + Sotutian: u : %*P : 27a.6km/h : : :-..!1'.,,ri..: r.:!.{ Fxample 2; Different animal species show a tremendous range o{ variation in their speed of movement. The fastesf land animal, the cheetah, can travel km /h..inconkast, the slowest aninral, a,species of sea crab, has.an average speed of just 5.7 km/y. How longf would it take the sei crab to trave11.00,0 km?. : Giaen: $verage speed (A) * S.f k*/y Total distance (d) : L00 km Unknown: Total time (f) Eqilation: t: # :ti Salution: t : :.17,5 y f "1,"' ': 1.,,. c al) :: Example 3: _You usually see lightning before you hear thund,er,' ' bggause light travels faster than Jound. Juan saw a flash o.f lighhring and heard the thunder 6 secon.ds later" Sound travels at a speed of 340 m/s in air. How far away was ]u.an from the lightring? Given: Average speed (F) : 340m/s Totaltime(ll.=66.,'r,,, ' LInknown: Iiotal clistance (d) Equation;'d-EXt r, Solutian: 6 : (340 m/s) x {6 s) : 2,M0 rn

5 Name Class Date Frastlce Exercises Exercise 1: In a boat race, Dan drove his motorboat over the 1000-meter course from start to finish in 40 seconds. What was Dan's average speed during flle race?, Exerciee 2: It takes serina O.lF hour to drive to school. Her route is 15 km long- what is serina'e avera$e speed on her drive to school? Exercise 3: In a competition, an athlete threw a flr,ine disk 139 meters through rhe air. while in flighi the disk kavelede!,an ave:aqe speed of 13.0 m7s. How long did the disk remain in nightt Exercise & T yo,r shout into Grand canyon, yoi,, voice travels * at -- the speed of sound (3a0 m/s) to tire bottom of tf," canyon and back, and you hear an echo. How deep is the Grand Canyon in a: spat where you can hear ylur echo S.Z seconds after you shout? Exercise 5: Sound travers m$ch faster in water than,air. It takbs 4.2 seconds for the sclund of an explosion to fraver underwater to a diver 6,006 m u*uy" what is the speed of J ' sound in water? =7

6 Name Class Date lnterpreting a Distance-Time Graph The distance-time graph below illustrates the motion of a car whose speed yaried with time during a trip. Calculate the average speed of the _car during the first 8 seconds of the trip. Give your answer in km/h. E soo t 4oo soo g 2oo.g 1oo Math Skill: Line Graphs and Conversion Factors You may want to read more about this Math Skill in tt t"ctrrir-""i Reference Handbook at the end of your textbook. Time (seconds) 1. Read and Understand What informntion are you ghsen? A graph of distance versus time. 2. PIan and Solve *tj!,you determine Iy speedfor the time interaal rderarceil in tne questrcn! L. To determine the distance travered in g s, move your finger up from the 8 s mark on the time axis to the plotted rine. 2. Now move your finger horizontally to the reft to the distance axis. Read the value from the axis. (ZOO m) 3, Calculate the average speed using the formuia Speed : Distancer/Time : 200 rn/g s : 25 m/s 4. Convert from m/s to km,/h: (25 m/sx3600 s/h)(l km/1000 m) = 90 km/h 3. Look Back and Check Is your answer reasonable? A quick calculation from the interval of constant speed shows that the car traveled 100 meters in 4 seconds-an average rp*a of 25 m/s. Math Practice On a separate sheet of paper, solae the follaaing problems. 1. How long did it take the car to travel a distance of 350 m? s 2. Determine the speed of the car in k*/h during the interval 0 s to 12 s.