Misalai 19 na Tambayoyi Masu Matsakaici
1. Duba jadawalin saurin (v) da lokaci (t) na wani abu da ke tafiya a layi madaidaiciya. Girman raguwar da abin ya fuskanta shine….
A. 2,5 ms-2
B. 3,5 ms-2
C. 4,0 ms-2
D. 5,0 ms-2
E. 6,0 ms-2
Tattaunawa
AB = hanzari akai-akai (motsin layi mai canza tsari ɗaya), BC = saurin akai-akai (motsin layi mai canza tsari ɗaya), CD = raguwa akai-akai (motsin layi mai canza tsari ɗaya).
Amsar da ta dace ita ce A.
2. Jadawalin da ke gefe jadawalin wani abu ne da ke tafiya a layi madaidaiciya. Nisa da abin ya yi tsakanin 0 da 8 s shine….
A. 72 m
B. 64 m
C. mita 48
D. 24 m
E. 12 m
Tattaunawa
Yi amfani da hanya ɗaya da matsalar da ta gabata, inda nisan ya yi tafiya = yankin yankin da aka yi inuwa a kan jadawalin. Ka lura da jadawalin da ke sama! An raba yankin da aka yi inuwa zuwa sassa domin a iya ƙididdige yankin ta amfani da dabarar da aka sani.
Yankin jirgin sama 1 = yankin alwatika = ½ (4-0)(12-0) = ½ (4)(12) = (2)(12) = 24
Yankin jirgin sama 2 = yankin murabba'i mai kusurwa huɗu = (8-4)(12-0) = (4)(12) = 48
Nisa da aka yi a lokacin daƙiƙa 8 = 24 + 48 = mita 72
Amsar da ta dace ita ce A.
3. Duba jadawalin saurin v da t don abin da ke gaba yana tafiya a layi madaidaiciya!
Nisan da aka yi a cikin daƙiƙa 12 shine….
A. 8 m
B. 10 m
C. mita 12
D. 24 m
E. 36 m
Tattaunawa
Wannan tambayar tana kama da ta baya. Duk da cewa tambayar da ta gabata ta yi tambaya game da nisan da aka yi tafiya a cikin daƙiƙa 10, wannan tambayar tana tambaya game da nisan da aka yi tafiya a cikin daƙiƙa 12.
4. Abu yana tafiya a layi madaidaiciya a gudun da ba ya canzawa na 36 km/h -1 na tsawon daƙiƙa 5, sannan yana sauri a hanzarin 1 m/s -2 na tsawon daƙiƙa 10 kuma yana raguwa a hanzarin 2 m/s -2 har sai abin ya tsaya. Jadawalin (vt) da ke nuna tafiyar abin shine...
Tattaunawa
An san cewa:
Motsi na 1 = GLB
Gudun da ba ya canzawa (v) = 36 km/h = 36 (m 1000) / 3600 s = 36.000 m / 3600 s = 10 m/s
Tazarar lokaci (t) = daƙiƙa 5
Motsi na 2 = hanzarta GLBB
Saurin farko (v)o) = saurin motsi 1 = 10 m/s
Hanzari (a) = 1 m/s2
Tazarar lokaci (t) = daƙiƙa 10
Motsi na 3 = GLBB mai raguwa
Hanzari (a) = -2 m/s2
Saurin ƙarshe (v)t) = 0 m/s
Ana nema: Jadawalin da ke nuna tafiyar wani abu
Amsa:
Ana iya tantance jadawalin bayan sanin saurin motsi na ƙarshe na 2 da kuma tazarar lokacin motsi na 3.
Saurin motsi na ƙarshe na 2:
vt = vo + a
vt = 10 + (1)(10) = 10 + 10 = 20 m/s
Saurin ƙarshe na motsi na 2 (v)t) = saurin farko na motsi 3 (vo) = 20 m/s
Tazarar lokaci na motsi 3:
vt = vo + a
0 = 20 + (-2)(t)
0 = 20 – 2t
20 = 2t
t = 20 / 2
t = daƙiƙa 10
Ka lura da jadawalin da ke sama.
Motsi na 1: Abu yana motsawa a gudun da ba ya canzawa na m10/s na tsawon daƙiƙa 5.
Motsi na 2: Abu yana sauri na tsawon daƙiƙa 10 har sai saurinsa ya kai 20 m/s
Motsi na 3: Ana rage gudu na abu na tsawon daƙiƙa 10 har sai ya tsaya.
Jadawalin da ya dace shine jadawalin da ke cikin amsar B.
Amsar da ta dace ita ce B.
5. Mota tana tafiya da farko a layi madaidaiciya a gudun da ba ya canzawa na 5 ms -1 . Bayan ta ci gaba da tafiyarta na tsawon daƙiƙa 10, motar tana tafiya da sauri ta yadda cikin daƙiƙa 5 masu zuwa za ta sami saurin gudu na 1 ms -2 . Sannan a kashe injin motar don motar ta tsaya bayan ta yi tafiya jimillar nisan mita 137,5. Ana iya kwatanta motsin motar da jadawalin gudu (v) da lokaci (t) wanda ya dace....
Tattaunawa
An san cewa:
Motsi na 1 = GLB
Gudun da ba ya canzawa (v) = 5 m/s
Tazarar lokaci (t) = daƙiƙa 10
Motsi na 2 = hanzarta GLBB
Saurin farko (v)o) = saurin motsi 1 = 5 m/s
Hanzari (a) = 1 m/s2
Tazarar lokaci (t) = daƙiƙa 5
Motsi na 3 = GLBB mai raguwa
Saurin ƙarshe (v)t) = 0 m/s
Jimlar nisan da aka yi tafiya (s) = 137,5 m/s
Ana nema: Jadawalin da ke nuna tafiyar wani abu
Amsa:
Nisa da motsi ya yi tafiya ta 1:
s = vt = (5)(10) = mita 50
Nisa da motsi ya yi tafiya ta 2:
s = vo t + ½ a2 = (5)(5) + ½ (1)(5)2 = 25 + ½ (25) = 25 + 12,5 = mita 37,5
Nisa da motsi ya yi tafiya ta 3:
137,5 – (50 + 37,5) = 137,5 – 87,5 = mita 50
Ana iya tantance jadawalin bayan sanin saurin motsi na ƙarshe na 2 da kuma tazarar lokacin motsi na 3.
Saurin ƙarshe na motsi na 2
Ana ƙididdige saurin motsi na ƙarshe na 2 ta amfani da bayanan motsi na 2.
vt = vo + a
vt = 5 + (1)(5) = 5 + 5 = 10 m/s
Saurin ƙarshe na motsi na 2 (v)t) = saurin farko na motsi 3 (vo) = 10 m/s
Tazarar lokaci na motsi 3
Ana iya ƙididdige tazarar lokaci bayan an san raguwar. Lissafin raguwar lokaci (a) da tazarar lokaci (t) yana amfani da bayanan motsi 3.
Rage guduwar abu a cikin motsi na 3:
vt2 = vo2 + 2 axles
02 = 102 + 2 a (50)
0 = 100 + 100 a
100 = -100 a
a = – 100/100
a = – 1 m/s2
Tazarar lokaci na motsi 3:
vt = vo + a
0 = 10 + (-1) t
0 = 10 – t
t = daƙiƙa 10
Ka lura da jadawalin da ke sama.
Motsi na 1: Abu yana motsawa a gudun da ba ya canzawa na m5/s na tsawon daƙiƙa 10.
Motsi na 2: Abu yana sauri na tsawon daƙiƙa 5 har sai saurinsa ya kai 10 m/s
Motsi na 3: Ana rage gudu na abu na tsawon daƙiƙa 10 har sai ya tsaya.
Amsar da ta dace ita ce D.
6. Mota mai nauyin kilogiram 800 tana tafiya a layi madaidaiciya tare da saurin farko na kilomita 36/h.-1 Bayan tafiyar mita 150, gudun zai zama kilomita 72/h-1Lokacin tafiyar motar shine…
A. Daƙiƙa 5
B. Daƙiƙa 10
C. daƙiƙa 17
D. daƙiƙa 25
E. daƙiƙa 35
Tattaunawa
An san cewa:
vo = 36 km/h = 36000 m/ 3600 s = 10 m/s
vt = 72 km/h = 72000 m/ 3600 s = 20 m/s
s = mita 150
An tambaya: lokacin tafiya (t)?
Amsa:
Akwai hanyoyi guda uku don saurin motsi na layi (GLBB) iri ɗaya:
vt = vo + a
s = vo t + ½ a2
vt2 = vo2 + 2 axles
Dangane da bayanan da aka sani, ba za mu iya ƙididdige lokacin tafiya kai tsaye ta amfani da ɗaya daga cikin dabarun da ke sama ba.
Da farko ana ƙididdige hanzarin (a) ta amfani da dabara ta 3.
vt2 = vo2 + 2 axles
202 = 102 + 2 a (150)
400 = 100 + 300 a
400 – 100 = 300 a
300 = 300 a
a = 300/300
a = 1 m/s2
Lissafa tazarar lokaci (t) ta amfani da dabara ta farko.
vt = vo + a
20 = 10 + (1) t
20 – 10 = t
t = daƙiƙa 10
Amsar da ta dace ita ce B.
7. Direban mota yana tafiya da gudun mita 20/s. Idan ya ga wani bugun gudu a gabansa, sai ya taka birki sannan motar ta tsaya bayan daƙiƙa 5. A ƙididdige nisan da motar ta yi!
Tattaunawa
An san cewa:
Saurin farko (v)o) = 20 m/s
Saurin ƙarshe (v)t) = 0 m/s
Tazarar lokaci (t) = daƙiƙa 5
An tambaya: nisan da aka yi tafiya (s)
Amsa:
Da farko a lissafta raguwar motar:
vt = vo + a
0 = 20 + a 5
-20 = 5a
a = -20/5
a = -4 m/s2
Lissafa nisan da motar ta yi:
s = vo t + 1/2 a2
s = (20)(5) + 1/2 (-4)(5)2 = (20)(5) + (-2)(25)
s = 100 – 50
s = mita 50
Nisan da motar ta yi tafiya mita 50 ne.
8. Kalli hoton da ke ƙasa.
Nisa da abin ya yi a lokacin t = daƙiƙa 40 shine…
A. 100 m
B. 160 m
C. mita 220
D. 280 m
E. 320 m
Tattaunawa
Yankin filin 1 = yankin murabba'i mai kusurwa huɗu = (20-0)(8-0) = (20)(8) = mita 160
Yankin jirgin sama 2 = yankin alwatika = ½ (25-20)(8-0) = ½ (5)(8) = (5)(4) = mita 20
Yankin jirgin sama 3 = yankin alwatika = ½ (30-25)(8-0) = ½ (5)(8) = (5)(4) = mita 20
Yankin filin 4 = yankin murabba'i mai kusurwa huɗu = (40-30)(8-0) = (10)(8) = mita 80
Nisa da aka yi a lokacin daƙiƙa 40 = 160 + 20 + 20 + 80 = mita 280
Amsar da ta dace ita ce D.
9. An nuna canjin saurin abin da ke motsawa na tsawon daƙiƙa 20 a cikin jadawalin vt da ke ƙasa!
Nisa da abu ya yi yayin da yake motsi shine…
A. 200 m
B. 260 m
C. mita 300
D. 400 m
E. 470 m
Tattaunawa
Yankin jirgin sama 1 = yankin alwatika = ½ (5-0)(20-0) = ½ (5)(20) = (5)(10) = mita 50
Yankin filin 2 = yankin murabba'i mai kusurwa huɗu = (15-5)(20-0) = (10)(20) = mita 200
Yankin jirgin sama 3 = yankin alwatika = ½ (20-15)(20-0) = ½ (5)(20) = (5)(10) = mita 50
Nisa da aka yi a lokacin daƙiƙa 20 = 50 + 200 + 50 = mita 300
Amsar da ta dace ita ce C.
10. Abu yana tafiya a layi madaidaiciya a gudun da ba ya canzawa na 36 km/h -1 na tsawon daƙiƙa 5, sannan yana sauri a hanzarin 1 m/s -2 na tsawon daƙiƙa 10 kuma yana raguwa a hanzarin 2 m/s -2 har sai abin ya tsaya. Jadawalin (vt) da ke nuna tafiyar abin shine...
Tattaunawa
An san cewa:
Motsi na 1 = GLB
Gudun da ba ya canzawa (v) = 36 km/h = 36 (m 1000) / 3600 s = 36.000 m / 3600 s = 10 m/s
Tazarar lokaci (t) = daƙiƙa 5
Motsi na 2 = hanzarta GLBB
Saurin farko (v)o) = saurin motsi 1 = 10 m/s
Hanzari (a) = 1 m/s2
Tazarar lokaci (t) = daƙiƙa 10
Motsi na 3 = GLBB mai raguwa
Hanzari (a) = -2 m/s2
Saurin ƙarshe (v)t) = 0 m/s
Ana nema: Jadawalin da ke nuna tafiyar wani abu
Amsa:
Ana iya tantance jadawalin bayan sanin saurin motsi na ƙarshe na 2 da kuma tazarar lokacin motsi na 3.
Saurin motsi na ƙarshe na 2:
vt = vo + a
vt = 10 + (1)(10) = 10 + 10 = 20 m/s
Saurin ƙarshe na motsi na 2 (v)t) = saurin farko na motsi 3 (vo) = 20 m/s
Tazarar lokaci na motsi 3:
vt = vo + a
0 = 20 + (-2)(t)
0 = 20 – 2t
20 = 2t
t = 20 / 2
t = daƙiƙa 10
Ka lura da jadawalin da ke sama.
Motsi na 1: Abu yana motsawa a gudun da ba ya canzawa na m10/s na tsawon daƙiƙa 5.
Motsi na 2: Abu yana sauri na tsawon daƙiƙa 10 har sai saurinsa ya kai 20 m/s
Motsi na 3: Ana rage gudu na abu na tsawon daƙiƙa 10 har sai ya tsaya.
Jadawalin da ya dace shine jadawalin da ke cikin amsar B.
Amsar da ta dace ita ce B.
11. Mota tana tafiya da farko a layi madaidaiciya a gudun da ba ya canzawa na 5 ms -1 . Bayan ta ci gaba da tafiyarta na tsawon daƙiƙa 10, motar tana tafiya da sauri ta yadda cikin daƙiƙa 5 masu zuwa za ta sami saurin gudu na 1 ms -2 . Sannan a kashe injin motar don motar ta tsaya bayan ta yi tafiya jimillar nisan mita 137,5. Ana iya kwatanta motsin motar da jadawalin gudu (v) da lokaci (t) wanda ya dace....
Tattaunawa
An san cewa:
Motsi na 1 = GLB
Gudun da ba ya canzawa (v) = 5 m/s
Tazarar lokaci (t) = daƙiƙa 10
Motsi na 2 = hanzarta GLBB
Saurin farko (v)o) = saurin motsi 1 = 5 m/s
Hanzari (a) = 1 m/s2
Tazarar lokaci (t) = daƙiƙa 5
Motsi na 3 = GLBB mai raguwa
Saurin ƙarshe (v)t) = 0 m/s
Jimlar nisan da aka yi tafiya (s) = 137,5 m/s
Ana nema: Jadawalin da ke nuna tafiyar wani abu
Amsa:
Nisa da motsi ya yi tafiya ta 1:
s = vt = (5)(10) = mita 50
Nisa da motsi ya yi tafiya ta 2:
s = vo t + ½ a2 = (5)(5) + ½ (1)(5)2 = 25 + ½ (25) = 25 + 12,5 = mita 37,5
Nisa da motsi ya yi tafiya ta 3:
137,5 – (50 + 37,5) = 137,5 – 87,5 = mita 50
Ana iya tantance jadawalin bayan sanin saurin motsi na ƙarshe na 2 da kuma tazarar lokacin motsi na 3.
Saurin ƙarshe na motsi na 2
Ana ƙididdige saurin motsi na ƙarshe na 2 ta amfani da bayanan motsi na 2.
v t = v o + a
v t = 5 + (1)(5) = 5 + 5 = 10 m/s
Saurin motsi na ƙarshe 2 (v t ) = saurin farko na motsi 3 (v o ) = 10 m/s
Tazarar lokaci na motsi 3
Ana iya ƙididdige tazarar lokaci bayan an san raguwar. Lissafin raguwar lokaci (a) da tazarar lokaci (t) yana amfani da bayanan motsi 3.
Rage guduwar abu a cikin motsi na 3:
v t 2 = v o 2 + 2 kamar yadda
0 2 = 10 2 + 2 a (50)
0 = 100 + 100 a
100 = -100 a
a = – 100/100
a = – 1 m/s 2
Tazarar lokaci na motsi 3:
v t = v o + a
0 = 10 + (-1) t
0 = 10 – t
t = daƙiƙa 10
Ka lura da jadawalin da ke sama.
Motsi na 1: Abu yana motsawa a gudun da ba ya canzawa na m5/s na tsawon daƙiƙa 10.
Motsi na 2: Abu yana sauri na tsawon daƙiƙa 5 har sai saurinsa ya kai 10 m/s
Motsi na 3: Ana rage gudu na abu na tsawon daƙiƙa 10 har sai ya tsaya.
Amsar da ta dace ita ce D.
12.
Jadawalin da ke hannun dama yana nuna wani abu yana tafiya a layi madaidaiciya. Nisa da abin ya yi tsakanin daƙiƙa 0 zuwa 8 shine….
A. 72 m
B. 64 m
C. mita 48
D. 24 m
E. 12 m
Tattaunawa
Yi amfani da hanya ɗaya da matsalar da ta gabata, inda nisan ya yi tafiya = yankin yankin da aka yi inuwa a kan jadawalin. Ka lura da jadawalin da ke sama! An raba yankin da aka yi inuwa zuwa sassa domin a iya ƙididdige yankin ta amfani da dabarar da aka sani.
Yankin jirgin sama 1 = yankin alwatika = ½ (4-0)(12-0) = ½ (4)(12) = (2)(12) = 24
Yankin jirgin sama 2 = yankin murabba'i mai kusurwa huɗu = (8-4)(12-0) = (4)(12) = 48
Nisa da aka yi a lokacin daƙiƙa 8 = 24 + 48 = mita 72
Amsar da ta dace ita ce A.
13.
Kula da jadawalin gudun v a kan t don abu yana motsawa a layi madaidaiciya a ƙasa!
Nisan da aka yi a cikin daƙiƙa 12 shine….
A. 8 m
B. 10 m
C. mita 12
D. 24 m
E. 36 m
Tattaunawa
Wannan tambayar tana kama da ta baya. Duk da cewa tambayar da ta gabata ta yi tambaya game da nisan da aka yi tafiya a cikin daƙiƙa 10, wannan tambayar tana tambaya game da nisan da aka yi tafiya a cikin daƙiƙa 12.
Yankin 1 = yankin alwatika = ½ (2-0)(4-0) = ½ (2)(4) = 4
Yankin jirgin sama 2 = yankin murabba'i mai kusurwa huɗu = (6-2)(4-0) = (4)(4) = 16
Yankin 3 = yankin alwatika = ½ (8-6)(4-0) = ½ (2)(4) = 4
Yankin 4 = yankin alwatika = ½ (10-8)(4-0) = ½ (2)(4) = 4
Faɗin 5 = faɗin murabba'i = (12-10)(4-0) = (2)(4) = 8
Nisa da aka yi a lokacin daƙiƙa 10 = 4 + 16 + 4 + 4 + 8 = mita 36
Amsar da ta dace ita ce D.
Tushen tambaya:
Tambayoyin Nazarin Fizik na Ƙasa ga Makarantar Sakandare ta Babbar Sakandare/Makarantar Sakandare ta Sana'a
Misalan tambayoyin motsi kai tsaye na uniform
14. Mota tana tafiya a layi madaidaiciya a gudun mita 10/s. Kayyade nisan da motar ta yi bayan ta yi tafiya na mita 10/s.
Tattaunawa
Gudun da ya dace na mita 10/daƙiƙa yana nufin motar tana tafiya mita 10 a kowace daƙiƙa 1.
Bayan daƙiƙa 2, babur ɗin zai yi tafiya ta nisan (2)(10) = mita 20,
Bayan daƙiƙa 3, babur ɗin zai yi tafiya ta nisan (3)(10) = mita 30,
Bayan daƙiƙa 10, babur ɗin zai yi tafiya ta nisan (10)(10) = mita 100.
Ƙara koyo a shafin misali na motsi madaidaiciya iri ɗaya
Misali na motsi mai sauri iri ɗaya na layi
15. Abu da farko yana hutawa yana motsawa tare da saurin gudu na 5 m/s akai-akai.2. Ƙayyade gudu da nisan da aka yi bayan daƙiƙa 5.
Tattaunawa
(a) Sauri bayan daƙiƙa 5
Saurin gudu na 5 m/s akai-akai2 Wannan yana nufin saurin yana ƙaruwa da m5/s a kowace daƙiƙa 1. Bayan daƙiƙa 2, saurin yana ƙaruwa zuwa m10/s. Bayan daƙiƙa 5, saurin yana ƙaruwa zuwa m25/s.
(b) Nisa da aka yi bayan daƙiƙa 5
An san cewa:
Saurin farko (v)o) = 0 (abun yana hutawa da farko).
Hanzari (a) = 5 m/s2
Tazarar lokaci (t) = daƙiƙa 5
An tambaya: nisan da aka yi tafiya (s)
Amsa:
s = vo t + ½ a2 = (0)(5) + ½ (5)(5)2) = 0 + (2,5)(25) = mita 62,5
Nisa da aka yi bayan daƙiƙa 5 ita ce mita 62,5.
16. Mota mai nauyin kilogiram 400 tana tafiya a layi madaidaiciya a saurin farko na kilomita 72/h. Bayan ta yi tafiya mita 100, saurinta ya karu zuwa kilomita 108/h. Lokacin da motar ke ɗauka don yin wannan nisan shine...
A. Daƙiƙa 1
B. Daƙiƙa 2
C. Daƙiƙa 3
D. Daƙiƙa 4
E. Daƙiƙa 5
Tattaunawa
An san cewa:
vo = 72 km/h = (72) (1000 m) / 3600 s = 20 m/s
vt = 108 km/h = (108) (1000 m) / 3600 s = 30 m/s
s = mita 100
An tambaya: tazarar lokaci (t)?
Amsa:
17. Jadawalin da ke gefe yana nuna motsin mota tana tafiya a layi madaidaiciya a daidai gwargwado. Nisan da motar ta yi a cikin daƙiƙa 8 shine...
A. 40 m
B. 60 m
C. mita 80
D. 100 m
E. 120 m
Tattaunawa
An san cewa:
vo = 10m/s
vt = 20m/s
t = daƙiƙa 8
An tambaya: Nisa aka yi tafiya (s)?
Amsa:
Amsar da ta dace ita ce E.
18. Jadawalin da ke gefe jadawalin wani abu ne da ke tafiya a layi madaidaiciya. Nisa da abin ya yi tsakanin daƙiƙa 0 zuwa 6 shine...
A. mita 40
B. mita 45
C. 50 mita
D. 55 m
E. mita 60
Tattaunawa
Nisa da aka yi tafiya = yankin jadawali (s = vt)
Nisa da aka yi tafiya 1 = ½ (10)(3) = (5)(3) = mita 15
Nisa da aka yi tafiya 2 = (10)(6-3) = (10)(3) = mita 30
Jimlar nisan da aka yi tafiya:
Mita 15 + mita 30 = mita 45
Amsar da ta dace ita ce B
Ƙara koyo a shafin misali don motsi mai sauri iri ɗaya.
Misali na motsi na faɗuwa kyauta
19. Mangoron ya faɗo daga tushe ya isa ƙasa bayan daƙiƙa 2. Saurin 'ya'yan itacen mangwaron lokacin da ya faɗi ƙasa shine... g = 10 m/s2
Tattaunawa
Idan hanzarin da aka samu saboda nauyi = 10 m/s2 Don haka mangwaro ko duk wani abu da ya faɗi cikin sauƙi yana samun ƙaruwar saurin mita 10/s a kowace daƙiƙa 1. Bayan daƙiƙa 2, saurin mangwaron shine mita 20/s.
Ƙara koyo a shafin misali na motsi na free fall
