Motsi tare da hanzari akai-akai - matsaloli da mafita

Matsalolin da aka Warware a Motsin Layi - Saurin sauri akai-akai

1. Mota tana sauri daga hutawa zuwa 20 m/s cikin daƙiƙa 10. Kayyade saurin motar!

Magani

An sani:

Saurin farko (v _o ) = 0 (hutu)

Tazarar lokaci (t) = daƙiƙa 10

Saurin ƙarshe (v _t ) = 20 m/s

Ana nema : Hanzari (a)

Magani:

v _t = v _o + a

20 = 0 + (a)(10)

20 = 10 a

a = 20/10

a = 2 m/s ²

[irp]

2. Mota tana raguwa daga mita 30/s zuwa hutawa cikin daƙiƙa 10. Kayyade saurin motar.

Magani

An sani:

Saurin farko (v _o ) = 30 m/s

Saurin ƙarshe (v _t ) = 0

Tazarar lokaci (t) = daƙiƙa 10

Ana so: hanzari (a)

Magani:

v _t = v _o + a

0 = 30 + (a)(10)

– 30 = 10 a

a = – 30/10

a = -3 m/s ²

Alamar mara kyau ta bayyana saboda saurin ƙarshe ya ƙasa da saurin farko.

[irp]

3. Mota tana farawa da sauri a daidai lokacin da take gudu da sauri 4 m/s ² a cikin daƙiƙa 1. Kayyade gudu da nisa bayan daƙiƙa 10.

Magani

(a) Sauri

Saurin gudu 4 m/s ² yana nufin ƙaruwar gudu 4 m/s a kowace daƙiƙa 1. Bayan daƙiƙa 2, saurin motar shine 8 m/s. Bayan daƙiƙa 10, saurin motar shine 40 m/s.

(b) Nisa

An sani:

Saurin farko (v _o ) = 0

Saurin ƙarshe (v _t ) = 40 m/s

Hanzari (a) = 4 m/s ²

Ana nema: Nisa

Magani:

s = v _o t + ½ a ² = 0 + ½ (4)(10 ² ) = (2)(100) = mita 200

[irp]

4. Mota tana tafiya a daidai gudun mita 10/s, sannan ta rage gudu a daidai gudun mita 2/s ^{2 har sai ta huta. A ƙayyade lokacin da ya wuce da kuma} nisan motar kafin ta huta.

An sani:

Saurin farko (v _o ) = 10 m/s

Hanzari (a) = -2 m/s ² (Alamar mara kyau ta bayyana saboda saurin ƙarshe ya ƙasa da saurin farko)

Saurin ƙarshe (v _t ) = 0 (hutu)

Ana so: Tazarar lokaci da nisa

Magani:

(a) Tazarar lokaci (t)

v _t = v _o + a

0 = 10 + (-2)(t)

0 = 10 – 2 t

10 = 2t

t = 10/2 = daƙiƙa 5

(b) Nisa

v _t ² = v _o ² + 2 kamar yadda

0 = 10 ² + 2(-2) s

0 = 100 – 4 s

100 = daƙiƙa 4

s = 100 / 4 = mita 25

[irp]

5. Mota tana tafiya a gudun mita 40/s, tana raguwa a gudun mita 4/s ² har sai ta huta. Kayyade gudu da nisa bayan raguwar gudu cikin daƙiƙa 10!

Magani

An sani:

Saurin farko (v _o ) = 40 m/s

Hanzari (a) = -4 m/s ²

Tazarar lokaci (t) = daƙiƙa 10

Ana so: saurin ƙarshe (v _t ) da nisa (s)

Magani:

(a) Saurin ƙarshe

v _t = v _o + a = 40 + (-4)(10) = 40 – 40 = 0 m/s

0 m/s yana nufin hutawa a mota.

(b) Nisa

s = v _o t + ½ a ² = (40)(10) + ½ (-4)(10 ² ) = 400 + (-2)(100) = 400 – 200 = mita 200

[irp]

6. Kayyade nisa bayan daƙiƙa 10!

Magani

Nisa: s = vt = (10-0)(5-0) = (10)(5) = mita 50

7. Kayyade nisa bayan daƙiƙa 4!

Magani

Nisa = murabba'in yanki + murabba'in yanki

Nisa = (8-0)(8-0) + ½ (16-8)(8-0) = (8)(8) + ½ (8)(8) = 64 + 32 = mita 96

8. Kayyade nisan motar bayan daƙiƙa 4!

Magani

Nisa = yanki mai kusurwa uku = ½ (4-0)(8-0) = ½ (4)(8) = mita 16

9. Wata mota tana tafiya a gudun kilomita 90/h ta wuce motar 'yan sanda da ta tsaya a gefen hanya. Minti daya bayan haka, motar 'yan sanda ta bi ta a ^gudun mita 0.8/s . Har yaushe motar 'yan sanda ta isa motar?

An sani:

Saurin mota (v) = 90 km/awa = mita 90,000 / daƙiƙa 3600 = mita 25/daƙiƙa

Tazarar lokaci (t) = minti 1 = daƙiƙa 60

Saurin motar 'yan sanda (a) = 0.8 m/s ²

Saurin farko na motar 'yan sanda (v _o ) = 0 m/s

Ana nema: Nisan da motar 'yan sanda ta yi tafiya

Magani:

Motar tana tafiya a daidai lokacin gudu. Nisa da mota ke tafiya:

Nisa ta farko:

s = vt = (25)(60) = mita 1500

Nisa ta ƙarshe:

s = vt = (25)(t)

Jimlar nisa = 1500 + 25 t

Motar 'yan sanda tana tafiya cikin sauri akai-akai. Nisa da motar 'yan sanda ta yi:

s = v _o t + ½ a ² = (0)(t) + ½ (0.8)(t ² ) = 0 + 0.4 t ² = 0.4 t ²

Idan motar 'yan sanda ta isa motar, nisan da motar 'yan sanda ta yi daidai yake da nisan da motar ta yi.

Nisa da mota ta yi = nisan da motar 'yan sanda ta yi

1500 + 25 t = 0.4 t ²

0.4 t ² – 25 t – 1500 = 0

Yi amfani da dabarar quadratic:

Nisan da motar 'yan sanda ta yi tafiya:

s = 0.4 t ² = (0.4)(100 ² ) = (0.4)(10,000) = mita 4000 s = 4 km

10. Mota tana motsawa a birki mai gudun mita 24/s akai-akai don ta sami raguwar gudu na mita 0.952/s akai - akai . ^2. Kayyade gudun motar bayan nisan mita 250.

An sani:

Saurin farko (v _o ) = 24 m/s

Hanzari (a) = – 0.952 m/s ² ( an sanya alama ta korau saboda raguwar gudu )

Nisa ( d ) = mita 250 a sakan daya

Ana Neman: Saurin mota bayan mita 250 a sakan daya

Magani:

Sananne: saurin farko (v_o), hanzari (a), distance (d), ana so: gudun ƙarshe (v_t) don haka yi amfani da lissafin v_t² = v_o² +2 ba d

v _t = saurin ƙarshe , v _o = saurin farko , a = hanzari , d = nisa

v _t ² = (24) ² + (2)(-0.952)(250)

v _t ² = 576 – 476

v _t ² = 100

v _t = √100

v _t = 10 m/s

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1. Nisa da ƙaura
2. Matsakaicin gudu da matsakaicin gudu
3. Gudun da ba ya canzawa
4. Ci gaba da hanzari akai-akai
5. Motsin faɗuwa kyauta
6. Motsin ƙasa a cikin faɗuwar 'free fall'
7. Motsin sama da ƙasa a cikin faɗuwar 'yanci