Yuav Lej Li Cas Nruab Nrab Ceev: 12 Kauj Ruam (nrog Duab)

2024 Tus sau: Jason Gerald | [email protected]. Kawg hloov kho: 2024-02-01 14:13

Txhua yam koj xav tau los xam qhov nruab nrab nrawm yog tag nrho kev txav chaw. lossis hloov txoj haujlwm, thiab sijhawm tag nrho. Nco ntsoov tias qhov nrawm kuj xam cov kev taw qhia thiab nrawm ntawm ib yam khoom, yog li suav nrog cov lus qhia hauv koj cov lus teb, xws li "sab qaum teb," "pem hauv ntej," lossis "sab laug." Yog tias koj qhov teeb meem kev suav nrawm tseem cuam tshuam nrog kev nrawm nrawm, koj tuaj yeem kawm txoj hauv kev nrawm los nrhiav cov lus teb txawm tias yooj yim dua.

Kauj ruam

Txoj Kev 1 ntawm 2: Xam Qhov Nruab Nrab Tshaj Tawm ntawm Kev Hloov Chaw thiab Sijhawm

Kauj Ruam 1. Nco ntsoov tias qhov nrawm nrawm suav nrog ob qho nrawm thiab kev taw qhia ntawm ib yam khoom

Tshaj tawm piav qhia tus nqi uas qhov khoom hloov pauv txoj haujlwm. Qhov no yuav tsum tsis tsuas yog nrawm npaum li cas cov khoom txav mus, tab sis kuj nrog nws cov lus qhia. "100 meters rau thib ob sab qab teb" yog tus nqi sib txawv dua li "100 metres thib ob sab hnub tuaj."

Cov naj npawb uas muaj kev taw qhia yog hu ua vector ntau '. Qhov ntau no tuaj yeem sib txawv los ntawm qhov tsis muaj qhov qhia tau hu ua scalar kom muaj nuj nqis los ntawm kev sau tus xub saum toj no qhov sib txawv. Piv txwv li, cov cim v sawv cev rau tus nqi, thaum cov cim v ^→ sawv cev rau qhov nrawm lossis nrawm + kev taw qhia. Cov cim sau v siv hauv kab lus no sawv cev rau kev nrawm.
Hauv cov teeb meem kev tshawb fawb, koj yuav tsum siv lub ntsuas ntsuas lossis lwm qhov ntsuas ntsuas los qhia kev nrug, thaum lub hom phiaj niaj hnub koj tuaj yeem siv txhua chav uas koj nyiam.

Xam Qhov Nruab Nrab Tshaj Tawm Kauj Ruam 2

Kauj Ruam 2. Nrhiav tus nqi txav chaw tag nrho

Kev tshem tawm yog qhov hloov pauv ntawm ib qho khoom lub luag haujlwm, lossis qhov nrug thiab kev taw qhia ntawm nws pib thiab xaus cov ntsiab lus. Cov kev taw qhia cov khoom txav ua ntej mus txog nws txoj haujlwm zaum kawg tuaj yeem tsis quav ntsej, vim tias tsuas yog qhov kev ncua deb nruab nrab ntawm qhov pib thiab xaus cov ntsiab lus raug coj mus rau hauv tus account. Rau thawj qhov piv txwv, peb yuav siv cov khoom txav ntawm qhov nrawm nyob hauv ib qho kev qhia:

Hais tias lub foob pob hluav taws txav mus rau sab qaum teb rau 5 feeb ntawm qhov nrawm ntawm 120 meters ib feeb. Txhawm rau suav qhov kawg, siv cov mis s = vt, lossis siv cov tswv yim xav los xam qhov kev nrug deb ntawm lub foob pob hluav taws tom qab ntawd (5 feeb) (120 meters/feeb) = 600 metres sab qaum teb los ntawm qhov pib.
Txog cov teeb meem cuam tshuam nrog kev nrawm nrawm, koj tuaj yeem daws lawv nrog s = vt + ntawm², lossis siv txoj hauv kev luv luv piav qhia hauv lwm ntu kom pom cov lus teb.

Xam Qhov Nruab Nrab Tshaj Tawm Kauj Ruam 3

Kauj Ruam 3. Nrhiav tag nrho lub sijhawm siv

Hauv peb qhov piv txwv, foob pob hluav taws tau txav mus rau tom ntej 5 feeb. Koj tuaj yeem nthuav qhia qhov nrawm nruab nrab hauv ib chav twg ntawm lub sijhawm, tab sis qhov thib ob yog chav haujlwm txuj ci thoob ntiaj teb. Peb yuav hloov chav nyob hauv vib nas this hauv qhov piv txwv no: (5 feeb) x (60 vib nas this/feeb) = 300 vib nas this.

Txawm tias muaj teeb meem kev tshawb fawb, yog tias lo lus nug siv teev lossis ntau dua ntawm lub sijhawm, nws yuav yooj yim dua los suav qhov nrawm ua ntej, tom qab ntawd hloov cov lus teb kawg rau meters/thib ob

Xam Qhov Nruab Nrab Tshaj Tawm Kauj Ruam 4

Kauj Ruam 4. Xam qhov nrawm nrawm raws li kev hloov chaw nyob rau lub sijhawm

Yog tias koj paub tias cov khoom txav mus deb npaum li cas, thiab nws yuav siv sij hawm ntev npaum li cas thiaj tuaj txog, koj yuav paub tias nws txav mus nrawm npaum li cas. Yog li rau qhov piv txwv peb tab tom siv, qhov nruab nrab nrawm ntawm lub foob pob hluav taws yog (600 metres sab qaum teb) / (300 vib nas this) = 2 meters/thib ob sab qaum teb.

Nco ntsoov suav nrog kev taw qhia (xws li "pem hauv ntej" lossis "sab qaum teb").
Hauv cov mis v_{ua av} = s/Δt. Lub cim delta txhais tau tias "hloov pauv", yog li s/meanst txhais tau tias "hloov pauv txoj haujlwm ib ntus."
Qhov nruab nrab nrawm tuaj yeem sau ua v_{ua av}, lossis raws li v nrog kab rov tav saum toj no nws.

Xam Qhov Nruab Nrab Tshaj Tawm Kauj Ruam 5

Kauj Ruam 5. Daws teeb meem nyuaj dua

Yog tias ib yam khoom hloov nws cov lus qhia lossis nrawm, tsis txhob poob siab. Qhov nruab nrab nrawm tseem "tsuas yog" xam los ntawm kev tshem tag nrho thiab tag nrho lub sijhawm. Dab tsi tshwm sim ntawm qhov pib thiab xaus cov ntsiab lus koj tuaj yeem tsis quav ntsej. Cov hauv qab no yog qee qhov piv txwv ntawm cov khoom mus nrog tib qho kev txav chaw thiab tag nrho lub sijhawm, thiab yog li, qhov nrawm nrawm ib yam:

Anna taug kev sab hnub poob ntawm 1 meter/s rau 2 vib nas this, tom qab ntawd sai li sai tau mus rau 3 meters/thib ob thiab txuas ntxiv mus rau sab hnub poob rau 2 vib nas this. Kev tshem tag nrho yog (1 m/s sab hnub poob) (2 sec) + (3 m/s sab hnub poob) (2 sec) = 8 metres sab hnub poob. Lub sijhawm tag nrho yog 2 vib nas this + 2 vib nas this = 4 vib nas this. Yog li qhov nruab nrab nrawm yog 8 meters sab hnub poob/ 4 vib nas this = 2 meters/thib ob sab hnub poob.
Bart taug kev sab hnub poob ntawm 5 metres/sec rau 3 vib nas this, tom qab ntawd tig ncig thiab taug kev sab hnub tuaj ntawm 7 meters/sec rau 1 thib ob. Peb tuaj yeem xav txog kev txav mus rau sab hnub tuaj li "tsis pom zoo rau sab hnub poob" yog li qhov kev tshem tawm tag nrho yog = (5 meters/sec sab hnub poob) (3 sec) + (-7 m/s sab hnub poob) (1 sec) = 8 meters. Lub sijhawm tag nrho = 4 vib nas this. Qhov nruab nrab ceev = 8 meters sab hnub poob / 4 vib nas this = 2 meters/thib ob sab hnub poob.
Charlotte taug kev sab qaum teb 1 meter thiab tom qab ntawd taug kev sab hnub poob 8 metres, tom qab ntawd sab qab teb 1 meter. Lub sijhawm nws yuav siv los ua kom tiav tag nrho cov lus yog 4 vib nas this. Kos daim duab rau ntawm ib daim ntawv, thiab koj yuav pom qhov kawg yog 8 metres sab hnub poob ntawm qhov pib, yog li tus nqi no yog kev txav chaw. Lub sijhawm tag nrho nws siv yog 4 vib nas this, yog li qhov nruab nrab nrawm yog 8 meters sab hnub poob / 4 vib nas this = 2 meters/thib ob sab hnub poob.

Txoj Kev 2 ntawm 2: Xam Qhov Nruab Nrab Tshaj Tawm ntawm Kev Ceev Ceev

Xam Qhov Nruab Nrab Tshaj Tawm Kauj Ruam 6

Kauj Ruam 1. Xav txog qhov pib nrawm thiab nrawm nrawm

Cia peb hais peb qhov teeb meem yog "Lub tsheb kauj vab tau txav mus rau sab xis nrog qhov nrawm ntawm 5 m/s, nrog qhov nrawm ntawm 2 m/s². Yog tias lub tsheb kauj vab no txav mus li 5 vib nas this, nws qhov nrawm npaum li cas?"

Yog hais tias chav tsev "meter/second"²"ua rau koj tsis meej pem, sau nws li" meters/second/second "lossis" meters per second per second. "Kev nrawm ntawm 2 meters/thib ob/thib ob txhais tau tias qhov nrawm tau nce ntxiv 2 meters ib pliag txhua thib ob.

Xam Qhov Nruab Nrab Tshaj Tawm Kauj Ruam 7

Kauj Ruam 2. Siv nrawm los nrhiav qhov nrawm tshaj

Kev nrawm, qhia los ntawm tus cim a, yog tus nqi ntawm kev hloov pauv nrawm (lossis tus nqi). Ceev nce ntawm qhov nce ntawm qhov nce ntxiv. Koj tuaj yeem kos lub rooj siv siv nrawm txhawm rau nrhiav qhov nrawm ntawm lub sijhawm sib txawv thoob plaws kev caij tsheb kauj vab. Peb yuav tsum tsim lub rooj no txhawm rau nrhiav qhov kawg ntawm qhov teeb meem (ntawm t = 5 vib nas this), tab sis peb yuav tsim lub rooj ntev los ua kom yooj yim rau koj kom nkag siab lub ntsiab lus no:

Thaum pib taw tes (lub sijhawm t = 0 vib nas this), lub tsheb kauj vab tau txav ntawm qhov nrawm ntawm 5 meters/s.
Tom qab 1 thib ob (t = 1), lub tsheb kauj vab tau txav ntawm qhov nrawm ntawm 5 meters/thib ob + ntawm = 5 meters/thib ob + (2 meters/thib ob)²) (1 thib ob) = 7 meters/thib ob.
Ntawm t = 2, lub tsheb kauj vab tau txav mus rau sab xis ntawm qhov nrawm ntawm 5+ (2) (2) = 9 meters/sec.
Ntawm t = 3, lub tsheb kauj vab tau txav mus rau sab xis ntawm qhov nrawm ntawm 5+ (2) (3) = 11 meters/sec.
Ntawm t = 4, lub tsheb kauj vab tau txav mus rau sab xis ntawm qhov nrawm ntawm 5+ (2) (4) = 13 meters/sec.
Ntawm t = 5, lub tsheb kauj vab tau txav mus rau sab xis nrog qhov nrawm ntawm 5+ (2) (5) = 15 meters/thib ob.

Xam Qhov Nruab Nrab Tshaj Tawm Kauj Ruam 8

Kauj Ruam 3. Siv cov mis no los nrhiav qhov nruab nrab nrawm

Yog tias thiab "tsuas yog" yog qhov nrawm nrawm, qhov nruab nrab nrawm yuav sib npaug nrog tus nqi nruab nrab ntawm qhov sib npaug ntawm qhov kawg thiab thawj qhov nrawm. (v_f +v_kuv)/2. Rau peb qhov teeb meem piv txwv saum toj no, qhov pib nrawm ntawm lub tsheb kauj vab yog v_kuv 5 meters/thib ob. Tom qab peb xam, qhov nrawm tshaj yog v_f 15 meters/thib ob. Ntxiv ob qhov txiaj ntsig no ua ke, peb tau txais (15 metres/thib ob + 5 meters/thib ob)/2 = (20 meters/thib ob)/2 = 10 meters/thib ob txoj cai.

Nco ntsoov suav nrog cov lus qhia, hauv qhov no "raug."
Lub sijhawm no tuaj yeem sau ua v₀ (tshaj tawm lub sijhawm 0, lossis pib tshaj tawm) thiab v (qhov tshaj tawm zaum kawg).

Xam Qhov Nruab Nrab Tshaj Tawm Kauj Ruam 9

Kauj Ruam 4. Nkag siab qhov ntsuas tus lej nruab nrab nrawm nrawm

Txhawm rau nrhiav qhov nrawm nrawm, peb tuaj yeem siv qhov nrawm ntawm txhua qhov chaw thiab nrhiav qhov nruab nrab rau txhua tus ntawm lawv. (Qhov no yog lub ntsiab lus ntawm qhov nruab nrab.) Hloov chaw ntawm kev siv txhua lub sijhawm, suav qhov nrawm nrawm ntawm ob lub ntsiab lus lub sijhawm thiab pom cov txiaj ntsig. Ib qho taw tes hauv lub sijhawm yog ze rau kev pib caij tsheb, qhov chaw tsheb kauj vab yuav maj mam mus, thiab lwm lub ntsiab lus nyob ze rau qhov kawg qhov chaw uas lub tsheb kauj vab yuav nrawm dua.

Xam Qhov Nruab Nrab Tshaj Tawm Kauj Ruam 10

Kauj Ruam 5. Kuaj qhov kev xav paub

Siv cov lus saum toj no los txiav txim qhov nrawm ntawm cov ntsiab lus sib txawv hauv lub sijhawm. Qee tus khub uas ua tau raws li peb cov txheej txheem yog (t = 0, t = 5), (t = 1, t = 4), lossis (t = 2, t = 3). Koj tuaj yeem sim cov mis no nrog t qhov tseem ceeb dua li cov lej ib yam, yog tias koj xav tau.

Qhov twg los xij ntawm cov ntsiab lus koj xaiv, qhov nrawm nruab nrab ntawm lub sijhawm ntawd yuav zoo ib yam. Piv txwv li, ((5+15)/2), ((7+13)/2), lossis ((9+11)/2) txhua qhov sib npaug 10 meters/sec rau sab xis

Xam Qhov Nruab Nrab Tshaj Tawm Kauj Ruam 11

Kauj Ruam 6. Ua kom tiav cov lus piav qhia nkag siab

Yog tias peb siv txoj hauv kev no nrog cov npe ntawm txhua lub sijhawm ua, peb yuav txuas ntxiv suav qhov nruab nrab ntawm thawj ib nrab ntawm kev mus thiab ib nrab ntawm kev mus ncig. Lub sijhawm nws yuav siv los npog txhua ib nrab yog qhov zoo ib yam, yog li tsis muaj qhov poob sai thaum peb suav tas.

Txij li ob tog yuav muab cov txiaj ntsig zoo ib yam, qhov nruab nrab ntawm cov nrawm no tseem yuav zoo ib yam. Hauv peb qhov piv txwv, qhov nrawm ntawm tag nrho yog "10 meters/sec rightward" tseem yuav yog 10 meters/sec sab xis.
Peb tuaj yeem pom qhov txiaj ntsig no los ntawm kev suav qhov nruab nrab ntawm ib khub, piv txwv li qhov pib thiab qhov nrawm kawg. Hauv peb qhov piv txwv, cov nrawm no tau mus txog t = 0 thiab t = 5, thiab tuaj yeem suav nrog siv cov qauv saum toj no: (5+15)/2 = 10 meters/sec rau sab xis.

Xam Qhov Nruab Nrab Tshaj Tawm Kauj Ruam 12

Kauj Ruam 7. Nkag siab cov lej no ua lej

Yog tias koj yooj yim dua nrog cov ntawv pov thawj sau ua cov qauv, koj tuaj yeem pib nrog tus lej txhawm rau xam qhov kev mus los uas xav tias nrawm dua, thiab muab cov mis los ntawm qhov ntawd:

s = vv_kuvt + ua². (Txuj ci s thiab t, lossis hloov pauv txoj haujlwm thiab hloov sijhawm, tab sis koj yuav nkag siab ib yam yog tias koj sau s thiab t.)
Qhov nruab nrab ceev v_{ua av} txhais ua s/t, yog li sau cov mis hauv daim ntawv s/t.
v_{ua av} = s/t = v_kuv + ntawm
Kev nrawm x sijhawm yog sib npaug rau kev hloov pauv tag nrho, lossis v_f -v_kuv. Yog li peb tuaj yeem hloov "ntawm" hauv cov mis, thiab tau txais:
v_{ua av} = v_kuv + (v_f -v_kuv).
Yooj yim: v_{ua av} = v_kuv + v_f -v_kuv = v_kuv + v_f = (v_f +v_kuv)/2.

Lub tswv yim

Kev nrawm nrawm sib txawv los ntawm kev nrawm vim tias qhov nrawm yog qhov muaj nuj nqis vector qhov ceev yog qhov ntau ntau. Cov khoom siv Vector cuam tshuam rau ob qho kev qhia thiab qhov loj, thaum cov nplai ntau ntxiv tsuas yog qhov loj me.
Yog tias qhov khoom txav mus nyob hauv ib qho me me, xws li sab laug-sab xis, koj tuaj yeem siv tus lej zoo los sawv cev rau ib qho kev taw qhia (xws li sab xis) thiab tus lej tsis zoo los sawv cev rau lwm qhov kev qhia (sab laug). Sau cov ntawv sau no rau saum koj nplooj ntawv kom pom meej rau cov neeg nyeem koj cov haujlwm.