Te nekehanga me te whakaterenga pumau – ngā raruraru me ngā otinga

Ngā Raru Whakatau i roto i te Nekehanga Raina – Te Whakaterenga Pūmau

1. Ka tere ake te tere o tētahi waka mai i te tū ki te 20 m/s i roto i te 10 hēkona. Tātaihia te tere o te waka!

otinga

Mōhiotia:

Te tere tīmatanga (v_o) = 0 (toenga)

Wā wā (t) = 10 hēkona

Te tere whakamutunga (v_t) = 20 m/s

hiahia : Te Whakaterenga (a)

Rongoā:

v_t = v_o + i

20 = 0 + (a)(10)

20 = 10

ā = 20 / 10

a = 2 m/s²

2. Kei te whakaheke tere te motuka mai i te 30 m/s ki te okioki i roto i te 10 hēkona. Tātaihia te whakaterenga o te motuka.

otinga

Mōhiotia:

Te tere tīmatanga (v_o) = 30 m/s

Te tere whakamutunga (v_t) = 0

Wā wā (t) = 10 hēkona

E hiahiatia ana: whakaterenga (a)

Rongoā:

v_t = v_o + i

0 = 30 + (a)(10)

– 30 = 10 a

ā = – 30 / 10

a = -3 m/s²

Ka puta te tohu kino nā te mea ko te tohu whakamutunga tere he iti iho i te tere tīmatanga.

3. Ka tīmata te motuka, ā, ka tere haere i te tere pumau 4 m/s² in 1 hēkona. Whakatauhia tere me te tawhiti i muri i te 10 hēkona.

otinga

(a) Tere

Whakaterenga 4 m/s² ko te tikanga ka piki te tere mā te 4 m/s ia 1 hēkona. I muri i te 2 hēkona, ko te tere o te motuka he 8 m/s. I muri i te 10 hēkona, ko te tere o te motuka he 40 m/s.

(b) Tawhiti

Mōhiotia:

Te tere tīmatanga (v_o) = 0

Te tere whakamutunga (v_t) = 40 m/s

Whakaterenga (a) = 4 m/s²

E hiahiatia ana: tawhiti

Rongoā:

s = v_o t + ½ i² = 0 + ½ (4)(10²) = (2)(100) = 200 mita

4. Ka tere te motuka i te 10 m/s pumau, kātahi ka whakaheke i te tere i te 2 m/s pumau² tae noa ki te okiokinga. Whakatauhia te wā i pau me te roa o te waka tawhiti i mua i te okiokinga.

Mōhiotia:

Te tere tīmatanga (v_o) = 10 m/s

Whakaterenga (a) = -2 m/s² (Ka puta te tohu kino nā te mea he iti iho te tere whakamutunga i te tere tīmatanga)

Te tere whakamutunga (v_t) = 0 (toenga)

E hiahiatia ana: Te wā me te tawhiti

Rongoā:

(a) Te wā (t)

v_t = v_o + i

0 = 10 + (-2)(t)

0 = 10 – 2 t

10 = 2 tāra

t = 10 / 2 = 5 hēkona

(b) Tawhiti

v_t² = v_o² + 2 ngā toki

0 = 10² + 2(-2) hēkona

0 = 100 – 4 hēkona

100 = 4 hēkona

s = 100 / 4 = 25 mita

5. E 40 m/s te tere o te haere o tētahi motuka, ā, ka whakaheke i te tere pumau o te 4 m/s² tae noa ki te okiokinga. Tāutuhia te tere me te tawhiti i muri i te whakahekenga i roto i te 10 hēkona!

otinga

Mōhiotia:

Te tere tīmatanga (v_o) = 40 m/s

Whakaterenga (a) = -4 m/s²

Wā wā (t) = 10 hēkona

E hiahiatia ana: te tere whakamutunga (v_t) me te tawhiti (s)

Rongoā:

(a) Te tere whakamutunga

v_t = v_o + i = 40 + (-4)(10) = 40 – 40 = 0 m/s

Ko te tikanga o te 0 m/s he okiokinga mō te motuka.

(b) Tawhiti

s = v_o t + ½ i² = (40)(10) + ½ (-4)(10)²) = 400 + (-2)(100) = 400 – 200 = 200 mita

6. Tātaitia te tawhiti i muri i te 10 hēkona!

otinga

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

7. Tātaitia te tawhiti i muri i te 4 hēkona!

otinga

Tawhiti = horahanga tapawhā + horahanga tapatoru

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

8. Whakatauhia te tawhiti o te motuka i muri i te 4 hēkona!

otinga

Tawhiti = horahanga tapatoru = ½ (4-0)(8-0) = ½ (4)(8) = 16 mita

9. Ka neke te motuka i te tere 90 km/h i mua i te motuka pirihimana e tū ana i te taha o te rori. Kotahi meneti i muri mai, ka whaia e te motuka pirihimana. at 0.8 m / s²Te tawhiti e tae atu ai te motuka pirihimanaes te motuka?

Mōhiotia:

Ko te tere o te motuka (v) = 90 km/h = 90,000 mita / 3600 hēkona = 25 mita/h

Wā wā (t) = 1 meneti = 60 hēkona

Te tere o te motuka pirihimana (a) = 0.8 m/s²

Te tere tīmatanga o te motuka a ngā pirihimana (v_o) = 0 m/s

E hiahiatia ana: Te tawhiti i haerea e te motuka a ngā pirihimana

Rongoā:

Ka neke te motuka i te tere pumau. Te tawhiti i haerea e te motuka:

Te tawhiti tīmatanga:

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

Te tawhiti whakamutunga:

s = vt = (25)(t)

Tapeke tawhiti = 1500 + 25 t

Ka tere tonu te neke o te motuka a ngā pirihimana. Te tawhiti i haerea e te motuka a ngā pirihimana:

s = v_o t + ½ i² = (0)(t) + ½ (0.8)(t²) = 0 + 0.4 t² = 0.4 t²

Ina tae te motuka a ngā pirihimana ki te motuka, ka rite te tawhiti i haerea e te motuka a ngā pirihimana ki te tawhiti i haerea e te motuka.

Te tawhiti i haerea e te motuka = te tawhiti i haerea e te motuka a ngā pirihimana

1500 + 25 tāra = 0.4 tāra²

0.4 t² – 25 tāra – 1500 = 0

Whakamahia te tātai tapawhā:

Te tawhiti i haerea e te motuka a ngā pirihimana:

s = 0.4 t² = (0.4)(100²) = (0.4)(10,000) = 4000 mitas= 4 km

10. A motokā neke i te tere pumau 24 m/s ngā pēki kia whai te whakaroa tonu o te 0.952 m/s². Whakatauhia te tere o te motuka ai muri i te tawhiti o te 250 metera.

Mōhiotia:

Te tere tīmatanga (v_o) = 24 m/s

whakaterenga (a) = – 0.952 m/s² (tohu kino nā te mea he whakaroa)

tawhiti (d) = 250 mitas

E hiahiatia ana: Te tere o te motuka i muri i te 250 mitas

Rongoā:

Mōhiotia: te tere tīmatanga (v_o), whakatere (a), tawhiti (d), e hiahiatia ana: te tere whakamutunga (v_t) nō reira whakamahia te whārite o v_t² = v_o² +2 ki d

v_t = tere whakamutunga, roto_o = tere tīmatanga, he = whakatere, d = tawhiti

v_t² = (24)² + (2)(-0.952)(250)

v_t² = 576 - 476

v_t² = 100

v_t = √100

v_t = 10m/s

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1. Te tawhiti me te nekehanga
2. Te tere toharite me te tere toharite
3. Tere pumau
4. Whakatere tonu
5. Nekehanga hinga noa
6. Te nekehanga ki raro i te hinganga kore utu
7. Te nekehanga ki runga, ki raro hoki i te hinganga kore utu