Disance, Time, an Spee p.noebook December 0, 08 The spee of an objec is a measure of how fas i is going. To know he spee of an objec we nee o measure isance an ime. Disance () is he amoun of space beween wo objecs or poins. i's usually measure in millimeers (mm), cenimeers (cm), meers (m), or kilomeers (km). Time () is he uraion beween wo eens. i's usually measure in secons (s), minues (min), hours (h), or years (a) Imagine riing in a car 80 km along a roa in one hour. You woul say you raelle 80 km/h. Were you going he same spee he whole ime? Maybe you speee up o 00 km/h o pass oher ehicles, or soppe for a snack. Oerall, uring he enire hour, your aerage spee was 80 km/h. How o we calculae aerage spee? aerage spee (a) is calculae by iiing he oal isance raele by he oal ime aken our final isance (where we ene up) Soling Problems Seps:. Wrie own gien informaion.. Wrie own he unknown ariable (he one you are soling for).. If necessary, rearrange he spee equaion for he unknown ariable. 4. Plug in he known alues, an heir unis, ino he equaion an sole for he unknown. Imporan reminers Only roun off a he ery en of he calculaions. Wach significan figures. Inclue he correc unis. our iniial isance (where we sare) ela i means he change in The unis for spee are always a isance measuremen per ime measuremen because he formula is For example, km/h, m/s So, wha's he ifference beween aerage spee an insananeous spee? Insananeous spee of an objec is is spee a a paricular momen in ime. This guy oesn' care wha your spee was a momen ago. All ha maers is your spee a he momen i was measure. Inro Soling Problems Le's ry an example Julia wans o show off her skaing skills so she oes a marahon skae aroun he ice a he QPlex, a isance 4.5 km. She has o slow own a couple of imes o skae roun Parker who keeps falling own. I akes her 0.6 h. Wha is Julia's aerage skaing spee?. Wrie own gien informaion. MacKenzie an Jae ake a rain rip o Hogwars. They noice ha here are signs marking he isance along he racks. Neer waning o miss a chance o o a lile science, hey ecie o measure he ime beween signs. The nex wo signs rea 0 km an 0 km. They recor he elapse ime as 90.6 s. Deermine he spee of he rain beween he wo signs in kilomeers per hour.. Wrie own gien informaion. 0 km 90.6 s How many sig ig? isance 4.5 km. Wrie own he unknown ariable (he one you are soling for). ime 0.6 h?. Wrie own he unknown ariable (he one you are soling for).. If necessary, rearrange he spee equaion for he unknown ariable. elociy? How o you feel abou hose unis?. If necessary, rearrange he spee equaion for he unknown ariable. 4. Plug in he known alues, an heir unis, ino he equaion an sole for he unknown. a 0 km 90.6 s 0.056 km/s we wan km/h rounwe offroun a heoff en Shoul firs? 4. Plug in he known alues, an heir unis, ino he equaion an sole for he unknown. How o we coner? a 4.5 km 0.6 h 0.056 km 60 s min s How many sig ig? 60 min 9 km/h h How many sig ig? 7. km/h Example Example Alex ges a summer job hering chickens. He loes science so he ecies o recor he chickens' moemens. He noes ha hey peck aroun a an aerage spee of abou 0 m/h for abou 7.0 h/. If he were a really goo herer an coul ge he chickens o rael in a sraigh line, wha isance, in kilomeers, coul he her rael in a week? For March break, Aina an Josi ecie o isi Spain an Germany One ay on he beach hey bump ino Richar who is builing a san casle. They all ecie o ge a snack a he hoel resauran which is.9 km away. The resauran closes in 5 minues. If hey can walk.4 m/s, will hey make i in ime?. Wrie own gien informaion.. Wrie own gien informaion. How o you feel abou hese unis?.9 km.4 m/s 0 m/h unis mus be he same change he easies one.9 km 000 m km unis mus be he same le's coner hem a he en How o you feel abou hese unis? 7.0 h. Wrie own he unknown ariable (he one you are soling for). 900 m?. Wrie own he unknown ariable (he one you are soling for).. If necessary, rearrange he spee equaion for he unknown ariable.?. If necessary, rearrange he spee equaion for he unknown ariable. 4. Plug in he known alues, an heir unis, ino he equaion an sole for he unknown. 4. Plug in he known alues, an heir unis, ino he equaion an sole for he unknown. 900 m.4 m/s 57.4 s (0 m/h)(7.0 h) 770 m 7.7 x 0 m How many sig ig? Wha unis o we wan? minues 57.4 s min 60 s min How many sig ig? Example Example 4
Disance, Time, an Spee p.noebook December 0, 08 Disance, Spee an Time Pracice. Huner ges his license an ecies o show off for Sami so he ears own Hampon Roa a 97 km/h. How much ime woul i ake him o rael 6.0 km?. Julia an Rachelle ecie o ry ou for he cross counry running eam. How far woul hey ge if hey can run 6 km/h for 5 min before collapsing?. Josh M ges a rie o school bu he car ges a fla ire on he way. He oesn wan o be lae for science class so runs he res of he way. If he is 5.0 km away an can run 5 km/h, how long will i ake him o ge here? 4. How much ime woul i ake Dax o walk km o McDonal s for an Angus burger if he walke a a rae of 4.5 km/h? 5. MacKenzie ecies o skip science class (acually, she woul neer o ha!) bu hen sees Ms. Jensen in he hallway so she akes off running. Wha is her aerage elociy if she goes 00 m own he hallway in 9.8 s? Gie your answer in m/s an km/h. 6. Josh M is saying oer a Parker s house an hey are coming home lae, pas heir curfew. As hey sneak in quiely, rying no o wake up his parens, hey slink up he sairs moing 0.7 m in 6.8 s. Fin heir spee. 7. The nigh before a big science quiz, Aina, Jose, Bianca an Defne ecie o suy ogeher bu insea en up waching chick flicks all nigh long. Now hey on' wan o wrie he quiz an are ragging hemseles o class. If heir spee is 0. m/s, how far will hey moe in 8 s? 8. Ma has borrowe his parens car wihou permission an is riing wihou a license. He sees hem ou walking an realizes ha hey will be home in abou 45 secons. He is 500 m from home an riing 5 m/s. Will she ge o he rieway before hey o? 9. Some girls are skaing a he QPlex an Richar hinks one of hem is cue an ecies o impress her by oing some ricks. Unforunaely, he is saring a her an crashes ino Kasey an innocen bysaner. He falls, making a fool of himself. Calculae how far he will slie on he ice if he were skaing a m/s an sli for.5 s. 0. Lochlan is prey pumpe abou some new Vans he s geing an can wai o buy hem. He runs across he parking lo o he sore a 4 m/s. If i akes him.5 s o reach he sore, how far away was he car parke? Pracice Disance, Spee an Time Pracice. Huner ges his license an ecies o show off for Sami so he ears own Hampon Roa a 97 km/h. How much ime woul i ake him o rael 6.0 km? ( 0.06 h). Julia an Rachelle ecie o ry ou for he cross counry running eam. How far woul hey ge if hey can run 6 km/h for 5 min before collapsing? ( km). Josh M ges a rie o school bu he car ges a fla ire on he way. He oesn wan o be lae for science class so runs he res of he way. If he is 5.0 km away an can run 5 km/h, how long will i ake him o ge here? ( 0 min) 4. How much ime woul i ake Dax o walk km o McDonal s for an Angus burger if he walke a a rae of 4.5 km/h? ( 0.44 h) 5. MacKenzie ecies o skip science class (acually, she woul neer o ha!) bu hen sees Ms. Jensen in he hallway so she akes off running. Wha is her aerage elociy if she goes 00 m own he hallway in 9.8 s? Gie your answer in m/s an km/h. (0. m/s; 6.6 km/ h) 6. Josh M is saying oer a Parker s house an hey are coming home lae, pas heir curfew. As hey sneak in quiely, rying no o wake up his parens, hey slink up he sairs moing 0.7 m in 6.8 s. Fin heir spee. (0.99 m/s) 7. The nigh before a big science quiz, Aina, Jose, Bianca an Defne ecie o suy ogeher bu insea en up waching chick flicks all nigh long. Now hey on' wan o wrie he quiz an are ragging hemseles o class. If heir spee is 0. m/s, how far will hey moe in 8 s? (5.6 m) 8. Ma has borrowe his parens car wihou permission an is riing wihou a license. He sees hem ou walking an realizes ha hey will be home in abou 45 secons. He is 500 m from home an riing 5 m/s. Will she ge o he rieway before hey o? (0 s, yes) 9. Some girls are skaing a he QPlex an Richar hinks one of hem is cue an ecies o impress her by oing some ricks. Unforunaely, he is saring a her an crashes ino Kasey an innocen bysaner. He falls, making a fool of himself. Calculae how far he will slie on he ice if he were skaing a m/s an sli for.5 s. (0 m) 0. Lochlan is prey pumpe abou some new Vans he s geing an can wai o buy hem. He runs across he parking lo o he sore a 4 m/s. If i akes him.5 s o reach he sore, how far away was he car parke? (85 m) Answers Wha's a graph? Graphs are use o isually communicae quaniaie informaion. A graph is easier o inerpre han a able or wrien paragraph. The inepenen ariable is ploe on he x axis. his is he ariable we change or naurally changes on is own Disance, Spee an Time Quiz The epenen ariable is ploe on he y axis. his is he one we measure All graphs MUST hae: labels on he x an y axes showing unis of measuremen a ile a he op inicaing he informaion graphe ) Tile ) Labels on Axes quaniy unis scale Wha's he epenen ariable? isance Quiz Graphing. Complee he able. i f Δ Iniial sae Final sae.0 s 7.0 s 0.0 m 8.0 m 0 min 5 min 0 o C 00 o C.0 h 9.0 h 00 kg 50 kg 5 min 55 min 0 L L Toal change Aerage rae of change. A car is raeling along a sraigh roa. The car is.4 km from home a 0:0 a.m. an 74.8 km from home a :50 a.m. How fas is he isance changing?. A waer ank has a olume of 800 L. I eelops a leak s afer being fille. Laer, 7 s afer being fille, he olume of waer in he ank is 6 L. How fas is he olume of waer changing? 4. A can of pop is aken ou of a refrigeraor an place on a couner. Afer 0.0 min, he rae of change of emperaure for he pop was foun o be 0.7 o C/ min. If he pop ha a emperaure of 5oC in he refrigeraor, fin is final emperaure. 5. Fin he rae of change in each graph. No 8 0:6 AM Rae of Change
Disance, Time, an Spee p.noebook December 0, 08 Changing Suen Performance Par A eacher, Mr. Ganong ecies o perform an experimen in which he hrows cany a suens o ry o improe heir performance. The resuls are shown below: Jimbo go 90% in mah an receie 4 canies Bey Sue go canies an her mah mark was 50% Bey Ann go 0% in mah an receie cany. Bubba go canies an ene up wih 70% in mah.. Organize he aa ino a char.. Graph he aa. Call his graph.. Consruc a bar graph o compare he boys o he girls. Call his graph. 4. Describe a siuaion in which a line graph is he bes ype of graph while in ohers a bar graph is bes. 5. Use Graph o eermine he rae of change. 6. Use Graph o preic he number of canies ha woul resul in a suen grae of 00%. 7. Preic he grae you woul expec from a suen who receie no canies. Line graphs are for cause an effec. Bar graphs are for comparisons. Changing suen performance Uniform moion means somehing is raeling a a consan spee. spee remains he same oer a perio of ime no speeing up or slowing own Changing Suen Performance Par Anoher eacher, inspire by Mr. Ganong's resuls, ecie o ry an experimen of his own. Mr. Meene hough he coul improe suen performance by ishing ou insuls when suens mae misakes. His resuls are shown below: SPEED Wha's he epenen ariable? spee Wha oes his graph show us? spee is he same a eery ime Shaynasy go 70% in mah an receie 4 insuls. K Ci go only insul an go 80% in mah. La A ene up wih 50% in mah an receie 0 insuls. Ciiilyn receie 7 insuls an go 60% in mah.. Organize he aa ino a char.. Graph he aa.. Use he graph o eermine he rae of change. 4. Use he graph o preic he number of insuls ha woul resul in a suen grae of 00%. 5. Preic he grae you woul expec from a suen who receie no insuls. 6. Compare he resuls of Mr. Ganong an Mr. Meene. If a suen receie he same number of canies as insuls, preic he effec on he suen's performance. DISTANCE Wha oes his graph show us? he change in isance is he same for all imes How coul his happen? Driing wih cruise conrol keeps your car moing a he same spee. Non uniform moion occurs when spee is NOT consan. spee changes speeing up or slowing own. Wha's he epenen ariable? spee SPEED Wha's he epenen ariable? isance Wha oes his graph show us? he change in spee is he same for all imes DISTANCE Wha's he epenen ariable? isance Wha oes his graph show us? he change in isance is NOT he same for all imes Changing suen performance par How coul his happen? Sepping on he gas or he brake causes your spee o change. Uniform an non uniform moion Slope in Disance Time Graphs Imagine he isance coere by a running whie aile eer is measure. Time (s) Disance (m) 0 0 6 4 4 50 5 65 6 78 Wha's he epenen ariable? isance Graph hese aa. Wha oes he graph show us? how he isance (epenen ariable) changes wih ime (inepenen ariable) Monioring Traffic Wha is slope? slope is how seep he line is in a graph slope rise run i shows how much y changes as x changes in a isance ime graph y is isance an x is ime in oher wors, i shows a change in isance ( ) as ime changes ( ) Wai a minue! slope of a isance ime graph is y oer x which is isance oer he ime Soun familiar? ha's spee How o we calculae spee? so... he slope of a isance ime graph is elociy Which one is fases? How can you ell? 00 Biking, Skaing, an Walking he greaer he slope, he greaer he spee (an ice ersa) Disance (m) 90 80 70 60 50 40 0 0 0 Biking Skaing Walking Monioring Traffic Slope 4 5 6 7 8 9 0 Time (s)
Disance, Time, an Spee p.noebook December 0, 08 Disance raelle by a hummer his graph shows he isance raelle each minue for 0 minues Describe he moion of he objec in each graph. Wha oes he graph ell us abou he moion of he hummer? spee is fairly consan uniform moion Graph Graph Graph Wha oes he slope of he line ell us? he spee i.e., a change in isance in a cerain perio of ime i? f? i? f How o we fin he slope? pick wo poins on he line of bes fi (as far apar as possible) label he poins an Wha is a line of bes fi? a line hrough mos poins ha shows he basic paern hese poins ell us he change in isance an he change in ime fin he coorinaes (x an y alues) for hese poins an plug hem ino he equaion Uniform moion? Yes. The change in isance is consan for all imes. Uniform moion? Yes. The change in isance is consan for all imes. Uniform moion? This objec is no moing. The isance oes no change. Remember slope escribes how seep he line is. Slope gies us los of informaion. slope rise run (9.0.0) km (9.0.0) min.0 km/min y y x x Which objec is moing fases? Graph How can you ell? Seeper slope Le's ry anoher example. Fin he spee of he eer. Describe he graph Calculaing slope Wha if he line isn' sraigh? Wha if you on' hae he graph? Freesyle swimming isance Line of bes fi Broken line graph Time (s) Freesyle isance (m) 0.0 0.0 5.0 9.5 0.0 8.5 5.0 7.0 0.0 5.5 5.0 45.0 Draw a line of bes fi for each graph. Graph Graph Graphing Graph Draw a graph an fin he spee of he swimmer. slope y y x x 45.0 9.5 5.0 5.0 5.5 0.0.775 How o you feel abou he significan igis?.8 m/s Graph he aa Measuring Spee Aciiy. From he aa in he able, preic which sroke is fases. Jusify your response.. Draw a graph for each sroke.. From he graph, ienify he fases sroke. Jusify your response. 4. Calculae he spee of each sroke. Graphing Pracice Measuring Spee 4
Disance, Time, an Spee p.noebook December 0, 08 For Chrismas break you an your family are aking a roa rip o Monreal. Neer waning o miss a chance o pracice science, you ecie o keep rack of your spee uring he rip. Table shows he aa you collece. Sage of rip Iniial oomeer reaing (km) Final oomeer reaing (km) Iniial ime (s) Final ime (s) 65. 660.7 8:04 8:4 660.7 660.7 8:4 8: Disance (m) 0 0 Fin he slope of each secion of he graph. Wha oes he slope in each secion ell us abou wha was happening? Secion he objec is moing fases (slope m/min) Secion he objec is no moing (slope 0 m/min ) 660.7 654. 8: :0 4 654. 654. :0 :5 0 0 0 40 50 Time (min) Secion he objec is moing slower han in secion (slope 0.5 m/min) 5 654. 6709.6 :5 :7 a) During which ime perios was he car moing? Calculae he spee uring each of hese separae ime perios. b) Calculae he aerage spee for he rip as a whole, from he beginning of Sage o he en of Sage 5. c) Explain he ifferences in your answers for (a) an (b). ) Draw a isance ime graph of he rip. Wha's happening? Can you ell he sory base on he graph? Posiion ime graph of a shor walk from home. Disance Time Graphing Quesions. a) How is aerage spee ifferen from insananeous spee? b) When woul hey be he same? Posiion (m from home) 0 Time (min) 4 6 5. Wha inerpreaion can be mae abou a moing car if he line on a isance ime graph? for he car has he following characerisics? a) a high or seep slope b) a low or less seep slope c) a zero slope. A car an a ruck rael along he same highway wih he car moing faser han he ruck. a) How o heir isances raelle compare afer he same lengh of ime? b) How o heir imes compare afer raelling he same isance? 4. A car leaes Boren Carleon, PEI, on is way across he Confeeraion Brige ino New Brunswick. The isances an imes from he oll booh in PEI are recore in Table. They inclue a shor srech of roa beyon he en of he.9 km brige. a) Plo a isance ime graph. Draw a line of bes fi. b) Using your graph, fin he isance raelle afer 5.0 min. c) Using your graph, fin he ime require o cross he brige. ) Was he spee consan uring he car s rip across he Confeeraion Brige? How o you know? e) Calculae he slope of he graph. Wha oes his slope represen? f) Wha was he spee of he car in km/h? Table : Trael from oll booh on Confeeraion Brige Time (min) Disance (km) 0.0 0.0.0.4 4.0 4.8 6.0 7. 8.0 9.6 0.0.0.0 4.4 Quesions Disance, Spee an Time Graphing Quiz Quiz 5