This chapter gets the ball rolling by discussing some fundamental physics measurements.

Transcription

1 Chapter Getting Started with Physics In This Chapter Laying dwn measurements Simplifying with scientific ntatin Practicing cnversins Drawing n algebra and trignmetry This chapter gets the ball rlling by discussing sme fundamental physics measurements. At its rt, physics is all abut making measurements (and using thse measurements as the basis f predictins), s it s the perfect place t start! I als walk yu thrugh the prcess f cnverting measurements frm ne unit t anther, and I shw yu hw t apply math skills t physics prblems. Measuring the Universe A great deal f physics has t d with making measurements that s the way all physics gets started. Fr that reasn, physics uses a number f measurement systems, such as the CGS (centiment-gram-secnd) system and the MKS (meter-kilgram-secnd) system. Yu als use the standard English system f inches and feet and s n that s the FPI (ftpund-inch) system. In physics, all measurements (except fr sme angles) have units, such as meters r secnds. Fr example, when yu measure hw far a hckey puck slid, yu need t measure bth the distance in centimeters and the time in secnds. Fr reference, Table - shws the primary units f measurement (and their abbreviatins) in the CGS system. (Dn t bther memrizing the nes yu re nt familiar with nw; yu can cme back t them later as needed.) Table - CGS Units f Measurement Measurement Unit Abbreviatin Length centimeter cm Mass gram g Time secnd s Frce dyne dyne (cntinued)

2 8 Part I: Applying Physics Table - (cntinued) Measurement Unit Abbreviatin Energy erg erg Pressure barye ba Electric current bit Bi Magnetism gauss G Electric charge franklin Fr These are the measuring sticks that will becme familiar t yu as yu slve prblems and triumph ver the math in this wrkbk. Als fr reference, Table - gives yu the primary units f measurement in the MKS system. Table - MKS Units f Measurement Measurement Unit Abbreviatin Length meter m Mass kilgram kg Time secnd s Frce Newtn N Energy Jule J Pressure Pascal P Electric current Ampere A Magnetism Tesla T Electric charge Culmb C Q. Yu re tld t measure the length f a racecar track using the MKS system. What unit(s) will yur measurement be in? A. The crrect answer is meters. The unit f length in the MKS system is the meter.

3 Chapter : Getting Started with Physics 9. Yu re tld t measure the mass f a marble using the CGS system. What unit(s) will yur measurement be in?. Yu re asked t measure the time it takes the mn t circle the Earth using the MKS system. What will yur measurement s units be? 3. Yu need t measure the frce a tire exerts n the rad as it s mving using the MKS system. What are the units f yur answer? 4. Yu re asked t measure the amunt f energy released by a firecracker when it expldes using the CGS system. What are the units f yur answer?

4 0 Part I: Applying Physics Putting Scientific Ntatin t Wrk Physics deals with sme very large and very small numbers. T wrk with such numbers, yu use scientific ntatin. Scientific ntatin is expressed as a number multiplied by a pwer f 0. Fr example, suppse yu re measuring the mass f an electrn in the MKS system. Yu put an electrn n a scale (in practice, electrns are t small t measure n a scale yu have t see hw they react t the pull f magnetic r electrstatic frces in rder t measure their mass) and yu measure the fllwing: kg What the heck is that? That s a lt f zers, and it makes this number very unwieldy t wrk with. Frtunately, yu knw all abut scientific ntatin, s yu can cnvert the number int the fllwing: kg That is, 9. multiplied by a pwer f 0, 0 3. Scientific ntatin wrks by extracting the pwer f 0 and putting it n the side, where it s handy. Yu cnvert a number t scientific ntatin by cunting the number f places yu have t mve the decimal pint t get the first digit in frnt f that decimal pint. Fr example, is because yu mve the decimal pint tw places t the right t get 5.0. Similarly, 500 is because yu mve the decimal pint tw places t the left t get 5.0. Check ut this practice questin abut scientific ntatin: Q. What is in scientific ntatin? A. The crrect answer is Yu have t mve the decimal pint five times t the right t get 3.7.

5 Chapter : Getting Started with Physics 5. What is in scientific ntatin? 6. What is in scientific ntatin? 7. What is in scientific ntatin? 8. What is in scientific ntatin?

6 Part I: Applying Physics Cnverting between Units Physics prblems frequently ask yu t cnvert between different units f measurement. Fr example, yu may measure the number f feet yur ty car ges in three minutes and thus be able t calculate the speed f the car in feet per minute, but that s nt a standard unit f measure, s yu need t cnvert feet per minute t miles per hur, r meters per secnd, r whatever the physics prblem asks fr. Fr anther example, suppse yu have 80 secnds hw much is that in minutes? Yu knw that there are 60 secnds in a minute, s 80 secnds equals three minutes. Here are sme cmmn cnversins between units: m = 00 cm = 000 mm (millimeters) km (kilmeter) = 000 m kg (kilgram) = 000 g (grams) N (Newtn) = 0 5 dynes J (Jule) = 0 7 ergs P (Pascal) = 0 ba A (Amp) =. Bi T (Tesla) = 0 4 G (Gauss) C (Culmb) = Fr The cnversin between CGS and MKS is almst always just a factr f 0, s cnverting between the tw is simple. But what abut cnverting t and frm the FPI system? Here are sme handy cnversins that yu can cme back t as needed: Length: m = 00 cm km = 000 m in (inch) =.54 cm m = in mile = 580 ft =.609 km Å (angstrm) = 0 0 m Mass: kg = 000 g slug = 4.59 kg u (atmic mass unit) = kg Frce: lb (pund) = N N = 0 5 dynes N = 0.48 lb Energy: J = 0 7 ergs J = ft-lb

7 Chapter : Getting Started with Physics 3 BTU (British Thermal Unit) = 055 J kwh (kilwatt hur)= J ev (electrn Vlt) = J Pwer: hp (hrsepwer) = 550 ft-lb/s W (Watt)= ft-lb/s Because cnversins are such an imprtant part f physics prblems, and because yu have t keep track f them s carefully, there s a systematic way f handling cnversins: Yu multiply by a cnversin cnstant that equals ne, and where the units yu dn t want cancel ut. Q. A ball drps 5 meters. Hw many centimeters did it drp? A. The crrect answer is 500 centimeters. T perfrm the cnversin, yu d the fllwing calculatin: 50. meters# 00 centimeters = 500 centimeters meters Nte that 00 centimeters divided by meter equals because there are 00 centimeters in a meter. In the calculatin, the units yu dn t want meters cancel ut. 9. Hw many centimeters are in.35 meters? 0. Hw many secnds are in.5 minutes?

8 4 Part I: Applying Physics. Hw many inches are in.0 meters?. Hw many grams are in 3.5 kg? Cnverting Distances Smetimes yu have t make multiple cnversins t get what yu want. That demands multiple cnversin factrs. Fr example, if yu want t cnvert frm inches t meters, yu can use the cnversin that.54 centimeters equals inch but then yu have t cnvert frm centimeters t meters, which means using anther cnversin factr. Try yur hand at this example questin that invlves multiple cnversins: Q. Cnvert 0 inches int meters. A. The crrect answer is 0.45 m.. Yu knw that inch =.54 centimeters, s start with that cnversin factr and cnvert 0 inches int centimeters: 0 in # 54. # cm = 5. 4 cm in. Cnvert 5.4 cm int meters by using a secnd cnversin factr: 0 in # 54. cm # m = m in 00 cm

9 Chapter : Getting Started with Physics 5 3. Given that there are.54 centimeters in inch, hw many centimeters are there in yard? 4. Hw many centimeters are in a kilmeter? 5. Hw many inches are in an angstrm, given that angstrm (Å) = 0 8 cm? 6. Hw many inches are in a meter, given that there are.54 cm in inch?

10 6 Part I: Applying Physics Cnverting Times Physics prblems frequently ask yu t cnvert between different units f time: secnds, minutes, hurs, and even years. These times invlve all kinds f calculatins because measurements in physics bks are usually in secnds, but can frequently be in hurs. Q. An SUV is traveling.78 0 kilmeters per secnd. What s that in kilmeters per hur? A. The crrect answer is 00 km/hr.. Yu knw that there are 60 minutes in an hur, s start by cnverting frm kilmeters per secnd t kilmeters per minute: -. km 60 sec 78# 0 # = 66. km/ minute sec minute. Because there are 60 minutes in an hur, cnvert this t kilmeters per hur using a secnd cnversin factr: -. km 60 sec 60 minutes 78# 0 # # = 00 km/ hr sec minute hur 7. Hw many hurs are in week? 8. Hw many hurs are in year?

11 Cunting Significant Figures Chapter : Getting Started with Physics Yu may plug numbers int yur calculatr and cme up with an answer like , but that number isn t likely t please yur instructr. Why? Because in physics prblems, yu use significant digits t express yur answers. Significant digits represent the accuracy with which yu knw yur values. 7 Fr example, if yu knw nly the values yu re wrking with t tw significant digits, yur answer shuld be.5, which has tw significant digits, nt , which has 3! Here s hw it wrks: Suppse yu re tld that a skater traveled 0.0 meters in 7.0 secnds. Nte the number f digits: The first value has three significant figures, the ther nly tw. The rule is that when yu multiply r divide numbers, the result has the number f significant digits that equals the smallest number f significant digits in any f the riginal numbers. S if yu want t figure ut hw fast the skater was ging, yu divide 0.0 by 7.0, and the result shuld have nly tw significant digits.4 meters per secnd. Zers used just t fill ut values dwn t (r up t) the decimal pint aren t cnsidered significant. Fr example, the number 3600 has nly tw significant digits by default. That s nt true if the value was actually measured t be 3600, f curse, in which case it s usually expressed as 3600.; the final decimal indicates that all the digits are significant. On the ther hand, when yu re adding r subtracting numbers, the rule is that the last significant digit in the result crrespnds t the right-mst clumn in the additin r subtractin. Hw des that wrk? Take a lk at this additin example: S is the result 4.83? N, it s nt. The has n significant digits t the right f the decimal pint, s the answer shuldn t have any either. That means yu shuld rund the value f the result up t 5. Runding numbers in physics wrks as it usually des in math: When yu want t rund t three places, fr example, and the number in the furth place is a five r greater, yu add ne t the third place (and ignre r replace with zers any fllwing digits). Q. Yu re multiplying.0 by 9.7. What shuld yur answer be, keeping in mind that yu shuld express it in significant digits? A. The crrect answer is 0.. The calculatr says that the prduct is Yur result has t have the same number f significant digits as the least number f any tw values yu multiplied. That s tw here (because f 9.7), s yur answer runds up t 0.

12 8 Part I: Applying Physics 9. What is 9.3 multiplied by 6., taking int accunt significant digits? 0. What is the sum f 7.9, 9, and 5.654, taking int accunt significant digits? Cming Prepared with Sme Algebra It s a fact f life: Yu need t be able t d algebra t handle physics prblems. Take the fllwing equatin, fr example, which relates the distance smething has traveled (s) t its acceleratin and the time it has been accelerated: s= at Nw suppse that the physics prblem actually asks yu fr the acceleratin, nt the distance. Yu have t rearrange things a little here t slve fr the acceleratin. S when yu multiply bth sides by and divide bth sides by t, here s what yu get: s = t t $ $ $ $ a t Cancelling ut and swapping sides, yu slve fr a like this: a s t = $

13 Chapter : Getting Started with Physics 9 S that s putting a little algebra t wrk. All yu had t d was mve variables arund the equatin t get what yu want. The same apprach wrks when slving physics prblems (mst f the time). On the ther hand, what if yu had t slve the same prblem fr the time, t? Yu wuld d that by rearranging the variables like s: t= s/ a The lessn in this example is that yu can extract all three variables distance, acceleratin, and time frm the riginal equatin. Shuld yu memrize all three versins f this equatin? Of curse nt. Yu can just memrize the first versin and use a little algebra t get the rest. The fllwing practice questins call n yur algebra skills: Q. The equatin fr final speed, v f, where the initial speed was v, the acceleratin was a, and the time was t is v f v = at. Slve fr acceleratin. A. The crrect answer is a= _ v f-vi/ t T slve fr a, divide bth sides f the equatin by time, t.. The equatin fr ptential energy, PE, f a mass m at height h, where the acceleratin due t gravity is g, is PE = m g h. Slve fr h.. The equatin relating final speed, v f, t riginal speed, v, in terms f acceleratin a and distance s is v f v = as. Slve fr s.

14 Chapter : Getting Started with Physics Physics prblems require yu t be able t wrk with sines, csines, and tangents. Here s what they lk like fr Figure -: sin θ = y/h cs θ = x/h tan θ = y/x Yu can find the length f ne side f the triangle if yu re given anther side and an angle (nt including the right angle). Here s hw t relate the sides: x = h cs θ = y/tan θ y = h sin θ = x tan θ h = y/sin θ = h/cs θ And here s ne mre equatin, the Pythagrean Therem. It gives yu the length f the hyptenuse when yu plug in the ther tw sides: h= x + y 5. Given the hyptenuse h and the angle θ, what is the length x equal t? 6. If x = 3 and y = 4, what is the length f h?

15 Part I: Applying Physics Answers t Prblems abut Getting Started with Physics The fllwing are the answers t the practice questins presented earlier in this chapter. Yu see hw t wrk ut each answer, step by step. a grams The unit f mass in the CGS system is the gram. b secnds The unit f time in the MKS system is the secnd. c Newtns The unit f frce in the MKS system is the Newtn. d ergs The unit f energy in the CGS system is the erg. e Yu have t mve the decimal pint three places t the right. f Yu have t mve the decimal pint five places t the left. g Yu have t mve the decimal pint seven places t the right. h Yu have t mve the decimal pint three places t the left. i 35 cm Cnvert.35 meters int centimeters: 35. m# 00 cm = 35 cm m j 75 sec Cnvert.5 minutes int secnds: 5. min # 60 sec = 75 sec min k 78.6 in Cnvert.0 meters int inches: 0. m # in = in m l 350 g Cnvert 3.5 kilgrams int grams: 000 g 35. kg# = 350 g kg

16 Chapter : Getting Started with Physics 3 m 9.4 cm. yard is 3 feet, s cnvert that t inches: 3 ft # in = 36 in ft. Use a secnd cnversin factr t cnvert that int centimeters: n km. Cnvert centimeter t meters: in 3 ft # # 54. cm = 9. 4 cm ft in cm m - # = 0. # 0 m 00 cm. Use a secnd cnversin factr t cnvert that int kilmeters: in. Cnvert angstrm t centimeters: m cm km - # # = 0. # 0 5 km 00 cm 000 m - 8 A # 0 cm = 0 A. Use a secnd cnversin factr t cnvert that int inches: p 39.3 in. Cnvert meter int centimeters: - 8 cm cm A # # 0. in = 40. # cm A m # 00 cm = 00 cm m. Use a secnd cnversin factr t cnvert that int inches: q 68 hurs. Cnvert week int days: 00 cm m # # in = in m 54. cm 7 days week # = 7 days week. Use a secnd cnversin factr t cnvert that int hurs: r 8760 hurs. Cnvert year int days: days week # # 4 hurs = 68 hurs week day 365 days year # = 365 days year. Use a secnd cnversin factr t cnvert that int hurs: 365 days year # # 4 hurs = 8760 hurs year day in

17 4 Part I: Applying Physics s 504. The calculatr says the prduct is has three significant digits, and 6. has fur, s yu use three significant digits in yur answer. That makes the answer 504. t 33. Here s hw yu d the sum: The value 9 has n significant digits after the decimal place, s the answer shuldn t either, making it 33 (3.554 runded up). u h = PE/mg Divide bth sides by mg t get yur answer. v w vf - v a = s Divide bth sides by a t get yur answer. s t - at = v. Subtract at / frm bth sides:. Divide bth sides by t t get yur answer. s- at = vt x v = m KE. Multiply bth sides by /m:. Take the square rt t get yur answer. m KE = v y x = h cs θ Yur answer cmes frm the definitin f csine. A 5. Start with the Pythagrean therem: h= x + y. Plug in the numbers, and wrk ut the answer: h= = 5

18 Chapter The Big Three: Acceleratin, Distance, and Time In This Chapter Thinking abut displacement Checking ut speed Remembering acceleratin Being able t cnnect displacement, speed, and acceleratin is fundamental t wrking with physics. These things cncern peple every day, and physics has made an rganized study f them. Prblems that cnnect displacement, speed, and acceleratin are all abut understanding mvement, and that s the tpic f this chapter putting numbers int the discussin. Yu ll ften find physics prblems abut cars starting and stpping, hrses racing, and rcket ships zming back and frth. And after yu finish this chapter, yu ll be a real pr at slving them. Frm Pint A t B: Displacement Displacement ccurs when smething mves frm here t there. Fr example, suppse that yu have a ball at the zer psitin, as in Figure -A. A meters Figure -: A mving ball. B meters Nw suppse that the ball rlls ver t a new pint, 3 meters t the right, as yu see in Figure -B. The ball is at a new lcatin, s there s been displacement. In this case, the displacement is just 3 meters t the right. In physics terms, yu ll ften see displacement referred t as the variable s. In this case, s = +3 meters.

19 6 Part I: Applying Physics Like any ther measurement in physics, displacement is always expressed in units, usually centimeters r meters, as in this example. Of curse, yu als can use kilmeters, inches, feet, miles, r even light years (the distance light travels in ne year 5,865,696,000,000 miles). The fllwing example questin fcuses n displacement. Q. Yu ve taken the pineers advice t G West. Yu started in New Yrk City and went west 0 miles the first day, 4 miles the next day, and then back east 9 miles n the third day. What is yur displacement frm New Yrk City after three days? A. s = 5 miles west f New Yrk City. Yu first went west 0 miles, s at the end f the first day, yur displacement was 0 miles west.. Next, yu went west 4 days, putting yur displacement at miles = 4 miles west f New Yrk City. 3. Finally, yu traveled 9 miles east, leaving yu at 4 9 = 5 miles west f New Yrk City. S s = 5 miles west f New Yrk City.. Suppse that the ball in Figure - nw mves meter t the right. What is its new displacement frm the rigin, 0?. Suppse that the ball in Figure -, which started 4 meters t the right f the rigin, mves 6 meters t the left. What is its new displacement frm the rigin in inches?

20 Reading That Speedmeter Chapter : The Big Three: Acceleratin, Distance, and Time In physics terms, what is speed? It s the same as the cnventinal idea f speed: Speed is displacement divided by time. 7 Fr example, if yu went a displacement s in a time t, then yur speed, v, is determined as fllws: v = s t Technically speaking, speed is the change in psitin divided by the change in time, s yu als can represent it like this if, fr example, yu re mving alng the x axis: v x xf- x = = t t - t f Q. Suppse that yu want t drive frm New Yrk City t Ls Angeles t visit yur uncle s family, a distance f abut 78 miles. The trip takes yu fur days. What was yur speed in miles per hur? A. v x f = = =. t x - x t - t f 8 97 miles per hur. Start by figuring ut yur speed (the distance traveled divided by the time taken t travel that distance): 78 miles = days. Okay, the speed is 695.5, but what? This slutin divides miles by days, s it s miles per day nt exactly a standard unit f measurement. S what is that in miles per hur? T determine that, yu cancel days ut f this equatin and put in hurs. Because 4 hurs are in a day, yu can multiply as fllws (nte that days cancel ut, leaving miles ver hurs, r miles per hur): 78 miles day # = miles per hur 4 days 4 hurs S yur speed was 8.97 miles per hur. That s yur average speed, averaged ver bth day and night.

21 8 Part I: Applying Physics 3. Suppse that yu used yur new SpeedPass t get yu thrugh the tllbths at bth ends f yur trip, which was 90 miles n the turnpike and tk yu hur and 5 minutes. On yur return hme, yu re surprised t find a traffic ticket fr speeding in the mail. Hw fast did yu g, n average, between the tllbths? Was the turnpike authrity justified in sending yu a ticket, given that the speed limit was 65 mph? 4. Suppse that yu and a friend are determined t find ut whse car is faster. Yu bth start yur trips in Chicag. Driving nnstp, yu reach Ls Angeles a distance f 08 miles in.9 days, and yur friend, als driving nnstp, reaches Miami a distance f 380 miles in 0.89 days. Whse car was faster? Putting Pedal t Metal: Acceleratin In physics terms, acceleratin is the amunt by which yur speed changes in a given amunt f time. In terms f equatins, it wrks like this: a = v t Given initial and final velcities, v and v f, and initial and final times ver which yur speed changed, t and t f, yu can als write the equatin like this: a v v f- v = = t t - t T get the units f acceleratin, yu divide speed by time as fllws: v f- v a = t - t f f distance/ time = = distance time time Distance ver time squared? Dn t let that thrw yu. Yu end up with time squared in the denminatr just because it s velcity divided by time that s smething yu get used t when slving physics prblems. In ther wrds, acceleratin is the rate at which yur speed changes because rates have time in the denminatr. S fr acceleratin, yu can expect t see units f meters per secnd, r centimeters per secnd, r miles per secnd, r feet per secnd, r even kilmeters per hur.

22 Chapter : The Big Three: Acceleratin, Distance, and Time 9 Q. Suppse that yu re driving at 75 miles an hur and suddenly see red flashing lights in the rearview mirrr. Great, yu think, and yu pull ver, taking 0 secnds t cme t a stp. Yu culd calculate hw quickly yu decelerated as yu were pulled ver (infrmatin abut yur law-abiding tendencies that, n dubt, wuld impress the fficer). S just hw fast did yu decelerate, in cm/sec? A. / sec a v 3350 cm = = = 68 cm/ sec t 0 secnds. First cnvert t miles per secnd: 75 miles hur minute - # # =. 008 =. 08 # 0 miles per secnd hur 60 minutes 60 secnds. Cnvert frm miles per secnd t inches per secnd: # 0 miles 580 feet # # inches = 38 in secnd mile ft secnd 3. Yur speed was 38 inches per secnd. What s that in centimeters per secnd? # 0 miles 580 feet inches # # #. 54 centimeters = 3350 cm secnd mile ft inch secnd 4. What was yur acceleratin? That calculatin lks like this: a v v - v = = t t - t f cm/ secnd = - =-68 cm/ sec 0 secnds f In ther wrds, 68 cm/sec, nt +68 cm/sec. There s a big difference between psitive and negative in terms f slving physics prblems and in terms f law enfrcement. If yu accelerated at +68 cm/sec instead f accelerating at 68 cm/sec, yu d end up ging 50 miles per hur at the end f 0 secnds, nt 0 miles per hur. In ther wrds, the sign f the acceleratin tells yu hw the speed is changing. A psitive acceleratin means that the speed is increasing in the psitive directin, and a negative acceleratin (als knwn as deceleratin) tells yu that the speed is increasing in the negative directin.

23 30 Part I: Applying Physics 5. A rcket ship is ging t land n the mn in exactly hurs. There s nly ne prblem: It s ging 7,000 miles an hur. What des its deceleratin need t be, in miles per secnd, in rder t land n the mn safely at 0 miles per hur? 6. Yu re stpped at a red light when yu see a mnster SUV careening tward yu. In a lightning calculatin, yu determine yu have 0.8 secnds befre it hits yu and that yu must be ging at least.0 miles an hur frward at that time t avid the SUV. What must yur acceleratin be, in miles per hur? Can yu avid the SUV? 7. A bullet cmes t rest in a blck f wd in.0 0 secnds, with an acceleratin f meters per secnd. What was its riginal speed, in meters per secnd? 8. The light turns red, and yu cme t a screeching halt. Checking yur stpwatch, yu see that yu stpped in 4.5 secnds. Yur deceleratin was miles per secnd. What was yur riginal speed in miles per hur?

24 Cnnecting Acceleratin, Time, and Displacement Chapter : The Big Three: Acceleratin, Distance, and Time Yu knw that yu can relate speed with displacement and time. And yu knw that yu can relate speed and time t get acceleratin. Yu als can relate displacement with acceleratin and time: s= a_ tf-ti 3 If yu dn t start ff at zer speed, yu use this equatin: s= v t t _ f- i + a_ tf-ti Q. Yu climb int yur drag racer, waving nnchalantly at the cheering crwd. Yu lk dwn the quarter-mile track, and suddenly the flag ges dwn. Yu re ff, getting a tremendus kick frm behind as the car accelerates quickly. A brief 5.5 secnds later, yu pass the end f the curse and pp the chute. Yu knw the distance yu went: 0.5 miles, r abut 40 meters. And yu knw the time it tk: 5.5 secnds. S just hw hard was the kick yu gt the acceleratin when yu blasted dwn the track? A. 6.6 meters/secnd. Yu knw that s= a t Yu can rearrange this equatin with a little algebra (just divide bth sides by t and multiply by ) t get a = s t. Plugging in the numbers, yu get a s ^40 metersh = = = 6. 6 meters/ secnd t ^55. secndsh What s 6.6 meters/secnd in mre understandable terms? The acceleratin due t gravity, g, is 9.8 meters/secnd, s this is abut.7 g. And that s quite a kick.

25 3 Part I: Applying Physics 9. The light turns green, and yu accelerate at 0 meters per secnd. After 5 secnds, hw far have yu traveled? 0. A stne drps under the influence f gravity, 9.8 meters per secnd. Hw far des it drp in secnds?. A car is ging 60 miles per hur and accelerating at 0 miles per hur. Hw far des it g in hur?. A mtrcycle is ging 60 miles per hur, and decelerating at 60 miles per hur. Hw far des it g in hur?

26 Chapter : The Big Three: Acceleratin, Distance, and Time An eagle starts at a speed f 50 meters per secnd and, decelerating at 0 meters per secnd, cmes t rest n a peak 5 secnds later. Hw far is the peak frm the eagle s riginal psitin? 4. A trailer breaks lse frm its truck n a steep incline. If the truck was mving uphill at 0 meters per secnd when the trailer brke lse, and the trailer accelerates dwn the hill at 0.0 meters per secnd, hw far dwnhill des the trailer g after 0 secnds? 5. A blck f wd is shting dwn a track at 0 meters per secnd and is slwing dwn because f frictin. If it cmes t rest in 0 secnds and 00 meters, what is its deceleratin, in meters per secnd? 6. A minivan puts n the brakes and cmes t a stp in secnds. If it tk 00 meters t stp, and decelerates at 0 meters per secnd, hw fast was it riginally ging, in meters per secnd?

27 34 Part I: Applying Physics Cnnecting Speed, Acceleratin, and Displacement Suppse yu have a drag racer whse acceleratin is 6.6 meters/secnd, and its final speed was 46.3 meters per secnd. What is the ttal distance traveled? This scenari sets yu up t use ne f the imprtant equatins f mtin: v f v = as = a (x f x ) This is the equatin yu use t relate speed, acceleratin, and distance. Q. A drag racer s acceleratin is 6.6 meters/secnd, and at the end f the race, its final speed is 46.3 meters per secnd. What is the ttal distance the drag racer traveled? A. s. a v = meters f = ^ h = ^ h. T slve this prblem, yu need t relate speed, acceleratin, and distance, s yu start with this equatin: v f v = as = a (x f x ). In this scenari, v is 0, which makes this equatin simpler: 3. Slve fr s: 4. Plug in the numbers: s = v f = as a v f s. a v = meters f = ^ h = ^ h S the answer is 409 meters, abut a quarter f a mile standard fr a drag racing track.

28 Chapter : The Big Three: Acceleratin, Distance, and Time A bullet is accelerated ver a meter-lng rifle barrel at an acceleratin f 400,000 meters per secnd. What is its final speed? 8. A car starts frm rest and is accelerated at 5.0 meters per secnd. What is its speed 500 meters later? 9. A rcket is launched at an acceleratin f 00 meters per secnd. After 00 kilmeters, what is its speed in meters per secnd? 0. A mtrcycle is ging 40 meters per secnd and is accelerated at 6 meters per secnd. What is its speed after 00 meters?

29 36 Part I: Applying Physics Answers t Prblems abut Acceleratin, Distance, and Time The fllwing are the answers t the practice questins presented earlier in this chapter. Yu see hw t wrk ut each answer, step by step. a s = 4 meters The ball was riginally at +3 meters and mved meter t the right = 4 meters. b s = 78.6 inches. The ball started at 4 meters and mved 6 meters t the left, putting it at =.0 meters with respect t the rigin.. Cnvert.0 meters int inches: c v = 7 miles an hur. The ticket was justified meters# inches = inches meter. It tk yu ne hur and fifteen minutes, r.5 hurs, t travel 90 miles.. Divide 90 miles by.5 hurs: 90 miles = 7 miles/ hur 5. hurs d Yur speed = 564 miles per day; yur friend s speed = 550 miles per day. Yu re faster.. Nte that t simply cmpare speeds, there s n need t cnvert t miles per hur miles per day will d fine. First, calculate yur speed:. Next, calculate yur friend s speed: 08 miles = 564 miles/ day 9. days 380 miles = 550 miles/ day 089. days S yu were faster than yur friend and prbably mre tired at the end f yur trip. e 6.6 x 0 4 miles per secnd. Start by cnverting 7,000 miles per hur int miles per secnd: 7, 000 miles hur minute # # = 47. miles per secnd hur 60 minutes 60 secnds. T land n the mn, v f must be 0 miles per secnd, and t f t = hurs, r 3600 secnds = 700 secnds, s: 3. Calculating this yields a v v - v = = t t - t f a v v f- v = = t t - t f = = = = 6. 6 # 0 miles per secnd f 4 S the rcket needs a cnstant deceleratin f miles per secnd in rder t land n the mn at a speed f 0 miles per secnd, tuching dwn lightly.

30 Chapter : The Big Three: Acceleratin, Distance, and Time 37 f miles per hur Yu will avid the cllisin.. Start by cnverting 0.8 secnds int hurs in rder t get all the quantities in units yu want, miles and hurs: minute hur secnds# # =. # 0 4 hurs 60 secnds 60 minutes. Calculate the acceleratin needed t get yu t.0 miles per hur: a v v f- v = = t t - t f = # 0-4 = 45. # 0 miles per hur 3 That s abut 0.05g, which is pssible fr any car. Yu ll avid the SUV. g v = a ( t) = 800 meters per secnd. Yu can calculate the change in speed, because it is acceleratin multiplied by time: v = a ( t) = = 800 meters per secnd. S if the bullet lst 800 meters per secnd f speed t cme t a rest (v = 0), it must have been ging 800 meters per secnd riginally. h v = a ( t) = 0 miles per hur. The change in speed is acceleratin multiplied by time, s:. Cnvert this result t miles per hur: i 5 meters v = a ( t) = = miles per secnd # 0 miles 60 secnds 60 minutes # # = 0 miles/ hur secnd minute hur. Yu want t relate distance t acceleratin and time, s use this equatin:. Plug in the numbers: s= a t s a t = = = 5 meters j 705 meters (that s 705 meters dwnward). T relate distance t acceleratin and time, yu use this equatin:. Substitute the numbers: s= a t s a t = = ^- 9. 8h = -705 meters k 65 miles. T relate distance t speed, acceleratin, and time, yu use this equatin: s= v t t _ f- i + a_ tf-ti. Plug in the numbers: s v t t a t t = 0_ f- i + _ f- i = ^ h + = 65 miles

31 38 Part I: Applying Physics l 30 miles. Yu want t relate distance t speed, acceleratin, and time, s yu use this equatin: s= v t t _ f- i + a_ tf-ti. Plug in the numbers: s v t t a t t = 0_ f- i + _ f- i = ^ h - = 30 miles m 5 meters. T cnnect distance with speed, acceleratin, and time, yu use this equatin: s= v t t _ f- i + a_ tf-ti. Plug in the numbers: s v t t a t t = 0_ f- i + _ f- i = ^ h - = 5 meters n 300 meters. T relate acceleratin t speed and time, use this equatin: s= v t t _ f- i + a_ tf-ti. Plug in the numbers: s v t t a t t = 0_ f- i + _ f- i = - = meters 0.5 meters per secnd. T relate acceleratin t speed and time, use this equatin: s = a t + v t. Slve fr a: _ s- v ti a = t 3. Plug in the numbers: _ s- v ti ^00-0 # 0h a = = =-05. meters per secnd t 0 p 76.6 meters per secnd. Start with this equatin:. Slve fr v 0 : 3. Plug in the numbers: s= v t t _ f- i + a_ tf-ti v s a t t 0 = ; - _ f- i E t - t v s a t t 0 = ; - _ f- i E t - t f f = meters per secnd

32 Chapter : The Big Three: Acceleratin, Distance, and Time 39 q v f = 894 meters per secnd. Start with this equatin: v f v = as = a (x f x ). v is 0, s that makes things easier. Plug in the numbers: 3. Take the square rt: r v f = 70.7 meters per secnd v f = as = 400,000.0 = 800,000 (meters per secnd) v f = 894 meters per secnd. Yu want t find speed in terms f distance and acceleratin, s use this equatin:. Plug in the numbers: 3. Take the square rt: s v f = 4470 meters per secnd v f v = as = a (x f x ) v f = as = = 5,000 (meters per secnd) v f = 70.7 meters per secnd. Yu want t find the speed f the rcket ship, having been given distance and acceleratin, s use this equatin: v f v = as = a (x f x ). 00 kilmeters is 00,000 meters, s plug in the numbers: v f = as = 00 00,000 =.0 x 0 7 (meters per secnd) 3. Take the square rt t get the rcket s speed: v f = 4470 meters per secnd t v f = 63. meters per secnd. T determine the mtrcycle s final speed, use this equatin: v f v = as. v 0 = 40 meters per secnd, s plug in the numbers: 3. That means that v f is 4. Take the square rt t get v f : v f 40 = as = 6 00 = 400 (meters per secnd) v f = 4000 (meters per secnd) v f = 63. meters per secnd