Mifananidzo yekufamba kwakatwasuka - matambudziko nemhinduro
1. Kureba kwegirafu (yakatwasuka) zvichienderana nenguva (yakatwasuka) sezvakaratidzwa mumufananidzo uri pazasi. Chinhu chiri padivi chinoratidzwa nenhamba…
Solution:
Nhamba 3, inoratidzwa nemutsetse wakatwasuka.
2. Kumhanya kwegirafu (kwakatwasuka) vs nguva (yakatsetseka) yekufamba pakumhanya kwakasimba . Kumhanya kwegirafu kwakakura sei?
Solution:
3. Mumwe munhu akafamba nemotokari kubva kuguta A kuenda kuguta B, zvinoratidzwa negirafu iri pazasi. Mutsetse wakamira sekukurumidza uye mutsetse wakatwasuka senguva. Ndeipi daro rakafambwa nemotokari mumaminitsi makumi matatu kusvika makumi matanhatu.
Zvinozivikanwa:
Kumhanya (v) = 40 km/awa
Nguva (t) = 60 - 30 = maminetsi 30 = maawa 0.5
Zvinodiwa: Kure
Solution:
Kureba = kumhanya x nguva yekupfuura
Kureba = (40 km/awa)(0.5 awa)
Nhambwe = makiromita makumi maviri
4. Kumhanya kwegirafu (mutsetse wakatwasuka) zvichienzaniswa nenguva (mutsetse wakatwasuka) kunoratidza kufamba kwemotokari kubva payakamira yozofamba kusvika yamira kwemasekonzi masere, sezvakaratidzwa mumufananidzo uri pazasi.
Nhambwe inofambirwa nemota kubva pamasekonzi mashanu kusvika kumasekonzi masere yakaita sei?
Solution:
Nzvimbo 1 = nzvimbo yetriangle CD = ½ (6-5) (40-20) = ½ (1) (20) = 10
Nzvimbo 2 = nzvimbo yetriangle DE = ½ (8-6) (20-0) = ½ (2) (20) = 20
Nzvimbo 3 = Nzvimbo ye square = (6-5)(20-0) = (1)(20) = 20
Nhambwe inofambwa nemota kubva pamasekonzi mashanu kusvika kumasekonzi masere = 10 + 20 + 20 = mamita makumi mashanu.
5. Kureba kwemasekonzi mashanu ekupedzisira zvichienderana negirafu iri pazasi ndekwekuti ….
Solution:
Nzvimbo 1 = nzvimbo yetriangle = ½ (6-5) (40-20) = ½ (1) (20) = 10
Nzvimbo 2 = nzvimbo ye rectangle = (9-5)(20-0) = (4)(20) = 80
Nzvimbo 3 = nzvimbo yetriangle = ½ (10-9) (20-0) = ½ (1) (20) = 10
Kureba kwemasekonzi mashanu ekupedzisira :
10 + 80 + 10 = mamita zana
6. Kumhanya kwegirafu vs nguva yekufamba kwemotokari kusina kufanana.
Kukurumidzisa kumwe chete kunoitika pa…
Solution:
v t = vo + pa
v t – v o = pa
a = v t – vo o / t
a = kukurumidza, v t = kumhanya kwekupedzisira, v o = kumhanya kwekutanga, t = nguva yepakati.
Kukurumidza AB = (25 – 20) / (20 – 0) = 5 / 20 = 1/4 = 0.25 m/s 2
Kukurumidza BC = (45 – 25) / (40 – 20) = 20 / 20 = 1 m/s 2
CD yekukurumidzira = (35 – 45) / (50 – 40) = 10 / 10 = 1 m/s 2
Kukurumidza DE = (25 – 35) / (70 – 50) = 10 / 20 = 1/2 = 0.5 m/s 2
Kukurumidza EF = (0 – 25) / (90 – 70) = 25 / 20 = 5/4 = 1.25 m/s 2
7. Ndeipi daro rakafambwa mumasekonzi gumi?
Zvinozivikanwa:
Kumhanya kwekutanga (v)o= = 0
Kumhanya kwekupedzisira (v t ) = 20 m/s
Nguva yepakati (t) = masekondi gumi nemashanu
Zvaidiwa:
Nhanho yakafambwa mumasekonzi gumi
Solution:
Maequations matatu ekufamba nekumhanya nguva dzose:
v t = vo + pa
d = vot + ½ pa 2
v t 2 = vo 2 + 2 ad
v t = kumhanya kwekupedzisira, v o = kumhanya kwekutanga, a = kukurumidza, t = nguva, d = daro
Kukurumidzisa (a):
v t = vo + pa
20 = 0 + a (4)
20 = 4 a
a = 20 / 4
a = 5 m/s 2
Kufamba daro mumasekondi gumi:
d = vot + ½ pa 2
d = (0)(10) + ½ (5)(10) 2
d = ½ (5)(100)
d = (5)(50)
d = mamita zana nemakumi mashanu
8. Kana chinhu chikakandwa chakamira pamusoro penyika, saka ndiyo girafu yekumhanya kunoitika nechinhu chacho.
mhinduro
Kana chinhu chichifamba chakamira kumusoro, kukurumidza kunoitika nechinhu kunokonzerwa nekukweva. Hukuru hwekukweva nekuda kwekukweva i9.8 m/s 2 uye divi rekukweva nekuda kwekukweva irwo riri pakati peNyika.
Kukurumidza kunogara kuchiitika kunoratidzwa nemutsetse wakatwasuka wakaenzana ne t axis uye wakatarisana ne a axis.
Mhinduro chaiyo ndiD.
9. Zvichibva pagirafu iri pazasi, sarudza daro rakafambwa nechinhu kwemasekondi makumi maviri.
A. 600 m
B. 500 m
C. 200 m
D. 100 m
mhinduro
Kufamba kwedaro pakati pemasekondi 0 - 10 = nzvimbo yesikweya + nzvimbo yetriangle
Nzvimbo yesikweya = (20-0)(10-0) = (20)(10) = 200 metres
Nzvimbo yetriangle = (1/2)(10-0)(40-20) = (1/2)(10)(20) = (5)(20) = mamita zana
Kufamba kwedaro remasekonzi 0 - 10 = mamita 200 + mamita 100 = mamita 300
Kufamba kwedaro remasekonzi gumi kusvika makumi maviri = nzvimbo yetriangle
Nzvimbo yetriangle = (1/2)(20-10)(40-0) = (1/2)(10)(40) = (5)(40) = mamita zana
Kufamba kwedaro remasekonzi 0 - 20:
Mamita mazana matatu + mamita mazana maviri = mamita mazana mashanu
Mhinduro chaiyo ndeiyi B.
10. Kufamba kwezvinhu zvitatu, chimwe nechimwe chinoratidzwa negirafu iri pazasi.
Sarudza chirevo chakakodzera chekufamba kwezvinhu zvitatu zvese.
Solution:
Girafu yechinhu 1 = Girafu yekukurumidzira (a) uye nguva (t)
Zvichibva pagirafu, chinhu chinofamba nekumhanya kunogara kuripo. Kumhanya kunogara kuripo kunoratidzwa nemutsetse wakatwasuka wakatarisana nechikamu chekumhanya (a).
Girafu yechinhu 2 = Girafu yekumhanya (v) uye nguva (a)
Zvichibva pagirafu, chinhu chinofamba nevelocity isingachinji. Velocity isingachinji inoratidzwa nemutsetse wakatwasuka wakatarisana neaxis yevelocity (v).
Girafu yechinhu 3 = Girafu yekutama (x) nenguva (a)
Zvichibva pagirafu, chinoramba chichichinja kana chinhu chiri pazororo.
Mhinduro chaiyo ndeinoti A.
11. Nzvimbo yechinhu chiri kufamba nepakati pe x-axis inoratidzwa negirafu rinotevera.
Girafu inoratidza kuti chinhu chinofamba nemwero usingachinji pakati penguva….
A. Masekondi mashanu kusvika gumi nemashanu nemasekondi makumi maviri nemashanu kusvika makumi matatu nemashanu
B. Masekondi 0-5 uye masekondi 35-40
C. Masekondi 15-25
D. Masekondi 0-5, masekondi 15-25 uye masekondi 35-40
Solution:
Masekondi 5-15 nemasekondi 25-35 = Kufamba kwechinhu nguva dzose hakuchinji kana chinhu chakazorora.
Masekondi 0-5, masekondi 15-25 uye masekondi 35-40 = chinhu chinofamba nekumhanya kwakafanana.
Mhinduro chaiyo ndiD.
12. Girafu rinotevera rinoratidza kumhanya kwebasa renguva rezvinhu zviviri zvinofamba zvakananga kubva panzvimbo imwe chete yekutanga. Mushure mekufamba kwemasekonzi t, zvinhu zvese zvinochinja nzvimbo imwe chete. Sarudza nguva uye kutama kwechinhu.
A. Masekondi mashanu nemamita makumi mashanu
B. Masekondi mashanu nemamita zana
C. Masekondi gumi nemamita makumi mashanu
D. Masekondi gumi nemamita zana
Solution:
Girafu 1 = kukurumidza nguva dzose
Nguva yepakati = masekondi gumi
Kureba = nzvimbo yetriangle = ½ (v)(t) = ½ (10-0)(20-0) = ½ (10)(20) = (5)(20) = mamita zana
Girafu 2 = kumhanya kusingachinji
Nguva yepakati = masekondi gumi
Kureba = nzvimbo ye sikweya = (v)(t) = (10-0)(10-0) = (10)(10) = mamita zana
Mhinduro chaiyo ndiD.
13. Zvichibva pagirafu iri pazasi, nguva iyo chinhu chinofamba nekumhanya nguva dzose uye nguva iyo chinhu chiri kuona kumhanya kukuru ndeye ….
A. Pakati pe0 ne t1, uye pakati pe t1 uye t2
B. Pakati pa t 1 na t 2 , uye pakati pa t 2 na t 3
C. Pakati pa t 2 na t 3 , uye pakati pa t 1 na t 2
D. Pakati pe0 ne t 1 , uye pakati pe t 2 ne t 3
Solution:
Kana girafu iri mutsetse wakatwasuka zvinoreva kuti kumhanya kwacho hakuchinji, kana girafu iri slash zvinoreva kuti kumhanya kwacho hakuchinji. Mutsetse uri kurereka, kumhanya kwacho kuri kukura.
0 – t 1 = kumhanya nguva dzose
t 1 – t 2 = kumhanya kusingachinji
t 2 – t 3 = kukurumidza nguva dzose
Mhinduro chaiyo ndeiyi B.
1. Mubvunzo: Chii chinomiririrwa negirafu yenzvimbo vs. girafu yenguva? Mhinduro: Kukwirira kwegirafu yenzvimbo vs. girafu yenguva kunomiririra kumhanya kwechinhu. Kukwirira kwakadzika kunoratidza kumhanya kwakakwirira, nepo mutsetse wakatsetseka (wakatsetseka) uchiratidza kuti chinhu chiri panze.
2. Mubvunzo: Pagirafu yekukurumidza vs. nguva, unoona sei kutama kwechinhu? Mhinduro: Kutama kwechinhu kunogona kuwanikwa nekuverenga nzvimbo iri pasi pekona (kana pakati pekona ne x-axis) pagirafu yekukurumidza vs. nguva.
3. Mubvunzo: Ungasiyanisa sei kufamba kwakafanana nekusafanana pagirafu yenzvimbo vs. nguva? Mhinduro: Pagirafu yenzvimbo vs. nguva, kufamba kwakafanana kunomiririrwa nemutsetse wakatwasuka (constant slope), nepo kufamba kusina kufanana kunoratidzwa nemutsetse wakakombama, zvichiratidza kuti kumhanya kuri kuchinja nekufamba kwenguva.
4. Mubvunzo: Mutsetse wakatwasuka uri pagirafu yekukurumidza vs. nguva unoratidza chii? Mhinduro: Mutsetse wakatwasuka uri pagirafu yekukurumidza vs. nguva unoratidza kuti chinhu chiri kufamba nekumhanya kwakasimba, kureva kuti, hachisi kukurumidza kana kudzikamisa mafambiro.
5. Mubvunzo: Kana girafu yekukurumidza vs. nguva iri pasi pe axis yenguva (negative velocity), inorevei? Mhinduro: Kana girafu yekukurumidza vs. nguva iri pasi pe axis yenguva, inoratidza kuti chinhu chiri kufamba nenzira yakatarisana negwara rekutarisa (rinowanzoonekwa serinoonekwa serinoonekwa).
6. Mubvunzo: Kukwidza kunomiririrwa sei pagirafu yekumhanya vs. nguva? Mhinduro: Pagirafu yekumhanya vs. nguva, kukwidza kunomiririrwa nekutsetseka kwegirafu. Kukwidza kwakanaka kunoratidza kukurumidza kwakanaka, kutsika kusina kunaka kunoratidza kukurumidza kusina kunaka (kana kudzikira), uye mutsetse wakatsetseka unoratidza kusakwidza.
7. Mubvunzo: Ko parabolic curve iri pagrafu yenzvimbo vs. nguva inoratidza chii? Mhinduro: Parabolic curve iri pagrafu yenzvimbo vs. nguva inoratidza kuti chinhu chacho chiri pasi pekumhanya nguva dzose. Chimiro che curve iyi chakafanana ne quadratic, chinoenderana ne kinematic equation .
8. Mubvunzo: Mugirafu yenzvimbo vs. nguva, ungaziva sei kana chinhu chiri kufamba mberi kana kumashure zvichienderana nenzvimbo yacho yekutanga? Mhinduro: Kana curve kana mutsetse uri pagirafu yenzvimbo vs. nguva uri kukwira (uchienda kumusoro), zvinoratidza kuti chinhu chiri kufamba mberi (kana kuti munzira yakanaka). Kana curve kana mutsetse uri kudzika (uchienda pasi), zvinoratidza kuti chinhu chiri kufamba kumashure (kana munzira yakaipa) zvichienderana nenzvimbo yacho yekutanga.
9. Mubvunzo: Chinhu chinodonha chichitaridzika sei pagirafu yekukurumidza vs. nguva? Mhinduro: Kune chinhu chinodonha chichidonha (tisingateereri kudzivirira kwemhepo), girafu yekukurumidza vs. nguva ingave mutsetse wakatwasuka une mutserendende wakanaka (kana uchitangira kubva pakuzorora) nekuda kwekumhanya kunogara kuripo nekuda kwesimba rinokwevera pasi. Mutserendende unomiririra kukosha kwekumhanya, uko paNyika kuri .
10. Mubvunzo: Kana chinhu chiri pazororo, girafu yekukurumidzira ichienzanisa nenguva yaro inotaridzika sei? Mhinduro: Kune chinhu chiri pazororo, girafu yekukurumidzira ichienzanisa nenguva yaro ingave mutsetse wakatwasuka pane axis yenguva, zvichiratidza kuti kukurumidzira kwacho kuri zero mukati menguva yacho yese.
