Kuyenda ndi kuthamanga kosalekeza - mavuto ndi mayankho

Mavuto Othetsedwa mu Linear Motion - Kuthamanga Kokhazikika

1. Galimoto imathamanga kuchokera pamalo opumula kufika pa 20 m/s mu masekondi 10. Dziwani kuthamanga kwa galimotoyo!

Anakonza

Zodziwika:

Liwiro loyambirira (v _o ) = 0 (kupuma)

Nthawi yopuma (t) = masekondi 10

Liwiro lomaliza (v _t ) = 20 m/s

Kufunidwa : Kufulumizitsa (a)

Yankho:

v _t = vo ₊ pa

20 = 0 + (a)(10)

20 = 10 a

a = 20 / 10

a = 2 m/s ²

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2. Galimoto ikuthamanga pang'onopang'ono kuchoka pa 30 m/s kuti ipumule mu masekondi 10. Dziwani liwiro la galimotoyo.

Anakonza

Zodziwika:

Liwiro loyambirira (v _o ) = 30 m/s

Liwiro lomaliza (v _t ) = 0

Nthawi yopuma (t) = masekondi 10

Kufunidwa: kufulumizitsa (a)

Yankho:

v _t = vo ₊ pa

0 = 30 + (a)(10)

– 30 = 10 a

a = – 30/10

a = -3 m/s ²

Chizindikiro chotsutsa chimawonekera chifukwa liwiro lomaliza ndi lochepera kuposa liwiro loyambirira.

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3. Galimoto imayamba ndi kuthamanga pa liwiro losasintha la 4 m/s ² mu sekondi imodzi. Dziwani liwiro ndi mtunda pambuyo pa masekondi 10.

Anakonza

(a) Liwiro

Kuthamanga kwa 4 m/s ² kumatanthauza kuwonjezeka kwa liwiro ndi 4 m/s sekondi imodzi iliyonse. Pambuyo pa masekondi awiri, liwiro la galimoto ndi 8 m/s. Pambuyo pa masekondi 10, liwiro la galimoto ndi 40 m/s.

(b) Mtunda

Zodziwika:

Liwiro loyambirira (v _o ) = 0

Liwiro lomaliza (v _t ) = 40 m/s

Kuthamanga (a) = 4 m/s ²

Kufunidwa: Kutali

Yankho:

s = vot ₊ ½ pa ² = 0 + ½ (4)(10 ² ) = (2)(100) = mamita 200

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4. Galimoto imayenda pa liwiro losasintha la 10 m/s, kenako imatsika pang'onopang'ono pa liwiro losasintha la 2 m/s ^{2 mpaka itapuma. Dziwani nthawi yomwe yadutsa komanso} mtunda wa galimoto musanapumule.

Zodziwika:

Liwiro loyambirira (v _o ) = 10 m/s

Kuthamanga (a) = -2 m/s ² (Chizindikiro chotsutsa chimawonekera chifukwa liwiro lomaliza ndi lochepera kuposa liwiro loyambirira)

Liwiro lomaliza (v _t ) = 0 (kupuma)

Kufunidwa: Nthawi ndi mtunda

Yankho:

(a) Nthawi yopuma (t)

v _t = vo ₊ pa

0 = 10 + (-2)(t)

0 = 10 - 2 t

10 = 2 t

t = 10 / 2 = masekondi awiri

(b) Mtunda

v _t ² = v _o ² + 2 monga

0 = 10 ² + 2(-2) s

0 = 100 – 4 masekondi

100 = masekondi 4

s = 100 / 4 = mamita 25

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5. Galimoto imayenda pa liwiro la 40 m/s, imatsika liwiro pa liwiro losasintha la 4 m/s ² mpaka itapuma. Dziwani liwiro ndi mtunda mukatha kutsika liwiro m'masekondi 10!

Anakonza

Zodziwika:

Liwiro loyambirira (v _o ) = 40 m/s

Kuthamanga (a) = -4 m/s ²

Nthawi yopuma (t) = masekondi 10

Kufunidwa: liwiro lomaliza (v _t ) ndi mtunda (s)

Yankho:

(a) Liwiro lomaliza

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

0 m/s amatanthauza kupuma kwa galimoto.

(b) Mtunda

s = vot ₊ ½ pa ² = (40)(10) + ½ (-4)(10 ² ) = 400 + (-2)(100) = 400 – 200 = mamita 200

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6. Dziwani mtunda pambuyo pa masekondi 10!

Anakonza

Mtunda: s = vt = (10-0)(5-0) = (10)(5) = mamita 50

7. Dziwani mtunda pambuyo pa masekondi 4!

Anakonza

Mtunda = malo ozungulira + malo ozungulira atatu

Mtunda = (8-0)(8-0) + ½ (16-8)(8-0) = (8)(8) + ½ (8)(8) = 64 + 32 = mamita 96

8. Dziwani mtunda wa galimoto patatha masekondi anayi!

Anakonza

Mtunda = malo amakona atatu = ½ (4-0)(8-0) = ½ (4)(8) = mamita 16

9. Galimoto ikuyenda pa liwiro la 90 km/h kudutsa galimoto ya apolisi yomwe imayima m'mbali mwa msewu. Patapita mphindi imodzi, galimoto ya apolisi ikuyamba kuthamanga pa ^liwiro la 0.8 m/s . Kodi galimoto ya apolisi imafika patali bwanji ndi galimotoyo?

Zodziwika:

Liwiro la galimoto (v) = 90 km/ola = 90,000 metres / masekondi 3600 = 25 metres/sekondi

Nthawi yopuma (t) = mphindi imodzi = masekondi 60

Kuthamanga kwa galimoto ya apolisi (a) = 0.8 m/s ²

Liwiro loyamba la galimoto ya apolisi (v _o ) = 0 m/s

Akufuna: Mtunda woyenda ndi galimoto ya apolisi

Yankho:

Galimoto imayenda mofulumira kwambiri. Mtunda woyenda ndi galimoto:

Mtunda woyambira:

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

Mtunda womaliza:

s = vt = (25)(t)

Mtunda wonse = 1500 + 25 t

Galimoto ya apolisi imayenda mofulumira kwambiri. Mtunda woyenda ndi galimoto ya apolisi:

s = vot ₊ ½ pa ² = (0)(t) + ½ (0.8)(t ² ) = 0 + 0.4 t ² = 0.4 t ²

Galimoto ya apolisi ikafika pagalimoto, mtunda womwe galimoto ya apolisi imayendera umakhala wofanana ndi mtunda womwe galimotoyo imayendera.

Mtunda woyenda ndi galimoto = mtunda woyenda ndi galimoto ya apolisi

1500 + 25 t = 0.4 t ²

0.4 t ² – 25 t – 1500 = 0

Gwiritsani ntchito njira ya quadratic:

Mtunda woyenda ndi galimoto ya apolisi:

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

10. Galimoto imayenda ndi mabuleki a 24 m/s osasinthasintha kotero kuti imachepa ndi 0.952 m/s ^2. Dziwani liwiro la galimotoyo mutayenda mamita 250.

Zodziwika:

Liwiro loyambirira (v _o ) = 24 m/s

Kuthamanga (a) = – 0.952 m/s ² ( kulembedwa ndi negative chifukwa cha kuchepa kwa liwiro )

Mtunda ( d ) = mamita 250 s

Kufunidwa: Liwiro la galimoto pambuyo pa 250 metres s

Yankho:

Chodziwika: liwiro loyamba (v_o), kuthamanga (a), mtunda (d), kufunidwa: liwiro lomaliza (v_t) choncho gwiritsani ntchito equation ya v_t² =v_o² + 2 a d

v _t = liwiro lomaliza , v _o = liwiro loyambirira , a = kufulumizitsa , d = mtunda

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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