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 (okiokinga)
Wā wā (t) = 10 hēkona
Te tere whakamutunga (vt ) = 20 m/s
E hiahiatia ana : Te whakaterenga (a)
Rongoā:
vt = v o + i
20 = 0 + (a)(10)
20 = 10
ā = 20 / 10
a = 2 m/s 2
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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 (vt ) = 0
Wā wā (t) = 10 hēkona
E hiahiatia ana: whakaterenga (a)
Rongoā:
vt = v o + i
0 = 30 + (a)(10)
– 30 = 10 a
ā = – 30 / 10
a = -3 m/s 2
Ka puta te tohu kino nā te mea he iti iho te tere whakamutunga i te tere tīmatanga.
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3. Ka tīmata te motuka, ā, ka tere ake i te 4 m/s 2 pūmau i roto i te 1 hēkona. Tātaihia te tere me te tawhiti i muri i te 10 hēkona.
otinga
(a) Tere
Ko te whakaterenga 4 m/s2 te tikanga ka piki ake 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 (vt ) = 40 m/s
Whakaterenga (a) = 4 m/s 2
E hiahiatia ana: Tawhiti
Rongoā:
s = v o t + ½ i te 2 = 0 + ½ (4)(10 2 ) = (2)(100) = 200 mita
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4. Ka tere te motuka i te tere pumau 10 m/s, kātahi ka whakaheke i te tere pumau 2 m/s2 tae noa ki te okiokinga. Tātaihia te wā i pau me te tawhiti o te motuka i mua i te okiokinga.
Mōhiotia:
Te tere tīmatanga (v o ) = 10 m/s
Tere (a) = -2 m/s 2 (Ka puta te tohu kino nā te mea he iti iho te tere whakamutunga i te tere tīmatanga)
Te tere whakamutunga (vt ) = 0 (okiokinga)
E hiahiatia ana: Te wā me te tawhiti
Rongoā:
(a) Te wā (t)
vt = v o + i
0 = 10 + (-2)(t)
0 = 10 – 2 t
10 = 2 tāra
t = 10 / 2 = 5 hēkona
(b) Tawhiti
v t 2 = v o 2 + 2 hei
0 = 10 2 + 2(-2) s
0 = 100 – 4 hēkona
100 = 4 hēkona
s = 100 / 4 = 25 mita
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5. E 40 m/s te tere o te haere o tētahi motuka, ka whakaheke tere i te 4 m/s 2 pūmau tae noa ki te okioki. Tātaihia te tere me te tawhiti i muri i te whakaheke tere i roto i te 10 hēkona!
otinga
Mōhiotia:
Te tere tīmatanga (v o ) = 40 m/s
Whakaterenga (a) = -4 m/s 2
Wā wā (t) = 10 hēkona
E hiahiatia ana: te tere whakamutunga (vt ) me te tawhiti (s)
Rongoā:
(a) Te tere whakamutunga
v t = v o + at = 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 i te 2 = (40)(10) + ½ (-4)(10 2 ) = 400 + (-2)(100) = 400 – 200 = 200 mita
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6. Tātaitia te tawhiti i muri i te 10 hēkona!
otinga
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. E neke ana tētahi motuka i te tere 90 km/h i mua i tētahi motuka pirihimana e tū ana i te taha o te rori. Kotahi meneti i muri mai, ka whaia e te motuka pirihimana te tere 0.8 m/s² . Kia pēhea te tawhiti e tae atu ai te motuka pirihimana ki 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 a ngā pirihimana (a) = 0.8 m/s 2
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 i te 2 = (0)(t) + ½ (0.8)(t 2 ) = 0 + 0.4 t 2 = 0.4 t 2
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 pirihimana
1500 + 25 t = 0.4 t 2
0.4 tāra 2 – 25 tāra – 1500 = 0
Whakamahia te tātai tapawhā:
Te tawhiti i haerea e te motuka a ngā pirihimana:
s = 0.4 t 2 = (0.4)(100 2 ) = (0.4)(10,000) = 4000 mita s = 4 kiromita
10. Ka neke te motuka i te tere pumau 24 m/s kia mau tonu te whakahekenga o te tere ki te 0.952 m/s2 . Tātaihia te tere o te motuka i muri i te tawhiti o te 250 mita.
Mōhiotia:
Te tere tīmatanga (v o ) = 24 m/s
Whakaterenga (a) = – 0.952 m/s 2 ( kua hainatia te tohu kino nā te mea kua whakaroahia )
Tawhiti ( d ) = 250 mita s
E hiahiatia ana: Te tere o te motuka i muri i te 250 mita s
Rongoā:
Mōhiotia: te tere tīmatanga (vo), whakatere (a), tawhiti (d), e hiahiatia ana: te tere whakamutunga (vt) nō reira whakamahia te whārite o vt2 = vo2 +2 ki d
v t = te tere whakamutunga , v o = te tere tīmatanga , a = te whakaterenga , d = te tawhiti
v t 2 = (24) 2 + (2)(-0.952)(250)
v t 2 = 576 – 476
v t 2 = 100
vt = √100
v t = 10 m/s
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- Te tawhiti me te nekehanga
- Te tere toharite me te tere toharite
- Tere pumau
- Whakatere tonu
- Nekehanga hinga noa
- Te nekehanga ki raro i te hinganga kore utu
- Te nekehanga ki runga, ki raro hoki i te hinganga kore utu
