Misali na motsi mai sauri iri ɗaya na layi

Misalai 10 na motsi mai sauri iri ɗaya

1. Motar ta fara tsayawa a tsaye. Bayan daƙiƙa 10, saurin motar ya ƙaru zuwa mita 20/s. Ka tantance saurin motar!
Tattaunawa
Babu tsari (amfani da dabaru) :
Saurin motar yana canzawa zuwa m20/s bayan daƙiƙa 10. Wannan yana nufin saurin motar yana ƙaruwa da m2/s a kowace daƙiƙa. Don haka, saurin motar shine m2/s a kowace daƙiƙa = m2/s a kowace daƙiƙa = m2/s a kowace daƙiƙa².
Amfani da dabarar :
An san cewa:
Saurin farko (v)_o) = 0 (motar tana tsaye)
Tazarar lokaci (t) = daƙiƙa 10
Saurin ƙarshe (v)_t) = 20 m/s
An tambaya: hanzarta motar (a)
Amsa:
Domin an san shi v_oa_t, t kuma an tambaya sannan a yi amfani da dabarar GLBB v_t = vo + a
v_t = v_o + a
20 = 0 + (a)(10)
20 = 10 a
a = 20/10
a = 2 m/s²
Girman saurin motar shine 2 m/s²Wannan yana nufin cewa saurin motar yana ƙaruwa da mita 2/s a kowace daƙiƙa 1.

2. Motar tana tafiya da farko da gudun mita 30/s, tana rage gudu har sai ta tsaya bayan daƙiƙa 10. Girman raguwar motar shine...
Tattaunawa
Ba tare da dabara ba (yi amfani da dabaru):
Gudun motar yana raguwa daga m30/s zuwa m0/s cikin daƙiƙa 10. Wannan yana nufin saurin motar yana raguwa da m3/s a kowace daƙiƙa. Don haka, raguwar motar shine m2/s a kowace daƙiƙa = m3/s.².
Amfani da dabarar:
An san cewa:
Saurin farko (v)_o) = 30 m/s
Saurin ƙarshe (v)_t) = 0
Tazarar lokaci (t) = daƙiƙa 10
An tambaya: rage gudu (a)?
Amsa:
Domin an san shi v_oa_t, t kuma an tambaya sannan a yi amfani da dabarar GLBB v_t = vo + a
v_t = v_o + a
0 = 30 + (a)(10)
– 30 = 10 a
a = – 30/10
a = 3 m/s²
Girman saurin motar shine -3 m/s²Wannan yana nufin saurin motar yana raguwa da mita 3/s a kowace daƙiƙa. Alamar mara kyau tana nuna cewa saurin motar yana raguwa.

3. Abu da farko yana hutawa yana motsawa tare da saurin gudu na 4 m/s akai-akai.². Ƙayyade gudu da nisan da aka yi bayan daƙiƙa 10.
Tattaunawa
(a) Sauri
Hanzari 4 m/s² Wannan yana nufin saurin abu yana ƙaruwa da m4/s a kowace daƙiƙa 1. Bayan daƙiƙa 2, saurin abu yana ƙaruwa da m8/s. Bayan daƙiƙa 10, saurin abu yana ƙaruwa da m40/s.
(b) Nisa da aka yi tafiya
Saurin farko (v)_o) = 0
Saurin ƙarshe (v)_t) = 40 m/s
a = 4 m/s²

Nisa:
s = v_o t + ½ a² = 0 + ½ (4)(10)²) = (2)(100) = mita 200
4. Abu da ke motsawa da farko a gudun da ya dace na 10 m/s yana fuskantar raguwar gudu na 2 m/s.² har sai ya tsaya. A ƙayyade tazarar lokaci da nisan da motar ke tafiya kafin ta tsaya.
Tattaunawa
An san cewa:
Saurin farko (v)_o) = 10 m/s
Hanzari (a) = -2 m/s² (idan yana raguwa to ana nuna masa alama mara kyau)
Saurin ƙarshe (v)_t) = 0 (abu yana tsayawa motsi)
Tambaya: Tazarar lokaci da nisan da aka yi kafin motar ta tsaya.
Amsa:
(a) Tazarar lokaci
Domin an san shi v_oa_t, a kuma an nemi t sannan a yi amfani da dabarar GLBB v_t = v_o + a
v_t = v_o + a
0 = 10 + (-2)(t)
0 = 10 – 2 t
10 = 2t
t = 10 / 2 = daƙiƙa 5
Tazarar lokaci kafin tsayawa = daƙiƙa 5.
(b) Nisa da aka yi tafiya
v_t² = v_o² + 2 axles
= 0 10² + 2(-2) s
0 = 100 – 4 s
100 = daƙiƙa 4
s = 100 / 4 = mita 25
Nisan da motar ta yi kafin ta tsaya mita 25 ne

5. Mota da ke tafiya da sauri na m40/s tana fuskantar raguwar gudu na m4/s akai-akai.²A tantance gudu da nisan da motar ta yi bayan ta yi kasa da na tsawon daƙiƙa 10.
Tattaunawa
An san cewa:
Saurin farko (v)_o) = 40 m/s
Hanzari (a) = -4 m/s²
Tazarar lokaci (t) = daƙiƙa 10
An tambaya: gudu (v)_t) da nisa (s) bayan rage gudu na tsawon daƙiƙa 10
Amsa:
(a) Gudun ƙarshe
v_t = v_o + a = 40 + (-4)(10) = 40 – 40 = 0 m/s
Bayan rage gudu na tsawon daƙiƙa 10, saurin motar zai canza zuwa 0 ko kuma motar ta tsaya.
(b) Nisa da aka yi tafiya
s = v_o t + ½ a² = (40)(10) + ½ (-4)(10)²) = 400 + (-2)(100) = 400 – 200 = mita 200
Nisa da motar ta yi bayan ta rage gudu na tsawon daƙiƙa 10 har sai ta tsaya ita ce mita 200.
6. Saurin (v) na abu da ke tafiya a layi madaidaiciya yana daidai da lokaci (t) kamar yadda aka nuna a cikin jadawalin v-t. Nisa da abin ya yi a cikin daƙiƙa 5 shine…

Tattaunawa
Nisa da aka yi tafiya (s) = vt = (10-0)(5-0) = (10)(5) = mita 50
7. Jadawalin da ke gefe yana nuna motsin mota yana tafiya a layi madaidaiciya a daidai gwargwado. Nisan da motar ta yi a cikin daƙiƙa 4 shine….

Tattaunawa
Nisa da aka yi tafiya = yankin murabba'i + yankin alwatika
Nisa da aka yi tafiya = (8-0)(8-0) + ½ (16-8)(8-0) = (8)(8) + ½ (8)(8) = 64 + 32 = mita 96
8. Jadawalin da ke gefe yana nuna mota tana tafiya a layi madaidaiciya a gudun da ba ya canzawa. Nisan da motar ta yi a cikin daƙiƙa 4 shine….

Tattaunawa
Nisa da aka yi tafiya = yankin alwatika = ½ (4-0)(8-0) = ½ (4)(8) = mita 16

9. Duba teburin da ke ƙasa!

Teburin da ke sama yana nuna abubuwa uku da ke motsi a cikin layi madaidaiciya a daidai gwargwado wanda ke rufe nisan iri ɗaya. Saurin ƙarshe na P da saurin farko na Q na abubuwan sune….

A. 20 ms ^-1 da 20 ms ^-1

B. 20 ms ^-1 da 28 ms ^-1

C. 20 ms ^-1 da 40 ms ^-1

D. 40 ms ^-1 da 20 ms ^-1

E. 40 ms ^-1 da 40 ms ^-1

Tattaunawa

Nisan da aka yi tafiya iri ɗaya ne, don haka da farko a ƙididdige nisan da aka yi da abu mai lamba 3.

Nisa da abu mai lamba 3 ya yi tafiya:

An san cewa:

Saurin farko (v _o ) = 0 m/s

Saurin ƙarshe (v _t ) = 30 m/s

Hanzari (a) = 3 m/s ²

An tambaya : Nisa

Amsa:

v _t ² = v _o ² + 2 kamar yadda

v _t ² – v _o ² = 2 kamar yadda

30 ² – 0 ² = 2 (3) s

900 – 0 = s 6

900 = daƙiƙa 6

s = 900 / 6

s = mita 150

Saurin ƙarshe na abu mai lamba 1:

An san cewa:

Saurin farko (v _o ) = 20 m/s

Hanzari (a) = 4 m/s ²

Nisa (s) = mita 150

Tambaya : Saurin ƙarshe (v _t )

Amsa:

v _t ² = v _o ² + 2 kamar yadda

v _t ² = 20 ² + 2 (4)(150)

v _t ² = 400 + 1200

v _t ² = 1600

v _t = 40 m/s

Saurin farko na abu mai lamba 2:

An san cewa:

Saurin ƙarshe (v _t ) = 50 m/s

Hanzari (a) = 3 m/s ²

Nisa (s) = mita 150

Tambaya : Saurin farko (v _o )

Amsa:

v _t ² = v _o ² + 2 kamar yadda

v _t ² – 2 kamar yadda = v _o ²

50 ² – 2(3)(150) = v _o ²

2500 – 900 = v _o ²

1600 = v _o ²

v _o = 40 m/s

Amsar da ta dace ita ce E.

10. Abubuwa uku suna tafiya a layi madaidaiciya a daidai gwargwado a kan saman da aka yi da siffa. Duk abubuwa uku suna tafiya da sauri iri ɗaya. Girman abubuwa uku bayan sun yi motsi na daƙiƙa 10 an nuna su a cikin tebur mai zuwa:

Bayanan P da Q da ke cikin teburin suna da ƙimar….

A. 6 da 140

B. 6 da 120

C. 4 da 120

D. 4 da 100

E. 1 da 100

Tattaunawa

Haɓaka abubuwa uku iri ɗaya ne, don haka da farko ƙididdige hanzarin abu na 1.

Haɓaka abu na 1:

An san cewa:

Saurin farko (v _o ) = 2 m/s

Saurin ƙarshe (v _t ) = 22 m/s

Nisa (s) = mita 120

An tambaya : Nisa

Amsa:

v _t ² = v _o ² + 2 kamar yadda

v _t ² – v _o ² = 2 kamar yadda

22 ² – 2 ² = 2 a (120)

484 – 4 = 240 a

480 = 240 a

a = 480/240

a = 2 m/s ²

Saurin farko na abu na 2:

An san cewa:

Hanzari (a) = 2 m/s ²

Saurin ƙarshe (v _t ) = 24 m/s

Nisa (s) = mita 140

Tambaya : Saurin farko (v _o )

Amsa:

v _t ² = v _o ² + 2 kamar yadda

24 ² = v _o ² + 2 (2)(140)

576 = v _o ² + 560

576 – 560 = v _o ²

16 = v _o ²

v _o = 4 m/s

Nisa daga abu na 3:

An san cewa:

Saurin farko (v _o ) = 0 m/s

Saurin ƙarshe (v _t ) = 20 m/s

Hanzari (a) = 2 m/s ²

An tambaya : Nisa ( s )

Amsa:

v _t ² = v _o ² + 2 kamar yadda

20 ² = 0 ² + 2 (2) s

20 ² = 2 (2) s

400 = daƙiƙa 4

s = 400/4

s = mita 100

Amsar da ta dace ita ce D.

Tambayoyi game da motsi mai sauri iri ɗaya na layi

1. Motar ta fara tsayawa a tsaye. Bayan daƙiƙa 5, saurin motar ya ƙaru zuwa mita 15/s. Ka tantance saurin motar!
2. Motar tana tafiya da farko da gudun mita 24/s, tana rage gudu har sai ta tsaya bayan daƙiƙa 3. Girman raguwar motar shine...
3. 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 10.
4. Abu da ke motsawa da farko a gudun da ya dace na 5 m/s yana fuskantar raguwar gudu na 5 m/s.² har sai ya tsaya. A ƙayyade tazarar lokaci da nisan da motar ke tafiya kafin ta tsaya.
5. Mota da ke tafiya da sauri na m30/s tana fuskantar raguwar gudu na m5/s akai-akai.²A tantance gudu da nisan da motar ta yi bayan ta yi kasa da na tsawon daƙiƙa 5.
6. Saurin (v) na abu da ke tafiya a layi madaidaiciya yana daidai da lokaci (t) kamar yadda aka nuna a cikin jadawalin v-t. Nisa da abin ya yi a cikin daƙiƙa 10 shine…

7. Jadawalin da ke gefe yana nuna motsin mota yana tafiya a layi madaidaiciya a daidai gwargwado. Nisan da motar ta yi a cikin daƙiƙa 4 shine….

8. Jadawalin da ke gefe yana nuna mota tana tafiya a layi madaidaiciya a gudun da ba ya canzawa. Nisan da motar ta yi a cikin daƙiƙa 4 shine….

[Turanci: Saurin gaggawa akai-akai - matsaloli da mafita ]