# Ngā Tauira o ngā Pātai Nekehanga Raina Āhua
Ko te Nekehanga Raina Taurite (GLB) he ariā taketake i roto i te ahupūngao. Ko te nekehanga o tētahi mea i runga i te ara tika i te tere pumau. Ko te tikanga kāore he whakaterenga, ā, ka noho pumau tonu te tere puta noa. Ka whakaratohia e tēnei tuhinga ētahi tauira o ngā raruraru GLB me ā rātou otinga hei āwhina i a koe ki te mārama ake ki tēnei ariā.
## Whakamāramatanga Taketake o te GLB
I mua i te urunga atu ki ngā tauira pātai, me arotake tuatahi tātou i ētahi ariā taketake o te Nekehanga Rārangi Kotahi. I roto i te Nekehanga Rārangi Kotahi, ko te whārite tere e tautuhia ana penei:
\[ v = \frac{s}{t} \]
Kei hea:
– Ko te tere te \( v \),
– Ko te tawhiti ko \( s \),
– Ko te wā te \( t \).
Nā te mea he pumau te tere, ka taea te whakaahua i te tawhiti i haerea mā te whakamahi i tētahi whārite rārangi:
\[ s = v \times t \]
me:
– Ko te tawhiti i haerea ko \( s \),
– Ko te tere pumau te \( v \),
– Ko te \( t \) te wā e hiahiatia ana.
### Ngā Pātai Tauira me te Kōrero
#### Pātai 1: Te Tatau i te Tawhiti
Pātai:
E 60 km/h te tere o te haere o tētahi waka mō ngā hāora e rua. Kia pēhea te tawhiti e haere ai te waka?
Otinga:
Mā te whakamahi i te tātai tawhiti taketake i roto i te GLB, \( s = v \times t \):
– Tere (\( v \)) = 60 km/h
– Te Wā (\( t \)) = 2 hāora
Te tawhiti i haerea (\( s \)):
\[ s = v \times t \]
\[ s = 60 \, \text{km/haora} \times 2 \, \text{haora} \]
\[ s = 120 \, \text{km} \]
Nō reira, ko te tawhiti i haerea e te motuka he 120 km.
#### Pātai 2: Te Tatau i te Wā
Pātai:
E neke ana tētahi kaihaerere i te tere pumau o te 5 km/h. Mēnā me haere ia i te tawhiti o te 15 km, kia pēhea te roa?
Otinga:
Mā te whakamahi i te tātai taketake mō te wā i roto i te GLB, \( t = \frac{s}{v} \):
– Tawhiti (\( s \)) = 15 kiromita
– Tere (\( v \)) = 5 km/h
Te wā e hiahiatia ana (\( t \)):
\[ t = \frac{s}{v} \]
\[ t = \frac{15 \, \text{km}}{5 \, \text{km/h}} \]
\[ t = 3 \, \text{jam} \]
Nō reira, ko te wā e hiahiatia ana e te kaihaerere he 3 hāora.
#### Pātai 3: Te Tatau i te Tere
Pātai:
E 18 kiromita te roa o te haerenga a te kaieke pahikara i roto i te 1.5 hāora. He aha te tere pumau o te kaieke pahikara?
Otinga:
Mā te whakamahi i te tātai taketake mō te tere i roto i te GLB, \( v = \frac{s}{t} \):
– Tawhiti (\( s \)) = 18 kiromita
– Te Wā (\( t \)) = 1.5 hāora
Tere (\( v \)):
\[ v = \frac{s}{t} \]
\[ v = \frac{18 \, \text{km}}{1.5 \, \text{haora}} \]
\[ v = 12 \, \text{km/h} \]
Nō reira, ko te tere pumau o te kaieke pahikara he 12 km/h.
#### Pātai 4: Te Huinga o te Tawhiti me te Wā
Pātai:
E 240 kiromita te tere o te tereina i te tere pumau. Mēnā e 3 hāora te roa hei whakaoti i te hauwhā tuatahi o te tawhiti, tatauhia te roa katoa e hiahiatia ana hei whakaoti i te haerenga katoa.
Otinga:
Tuatahi, ka tatauhia e mātou te tawhiti o te hauwhā (1/4) o te haerenga katoa:
\[ s_1 = \frac{1}{4} \times 240 \, \text{km} \]
\[ s_1 = 60 \, \text{km} \]
E 60 kiromita te roa o te tereina i roto i ngā hāora e 3. Nō reira, ko te tere o te tereina:
\[ v = \frac{60 \, \text{km}}{3 \, \text{haora}} \]
\[ v = 20 \, \text{km/h} \]
Muri iho, ka tatauhia e mātou te roa katoa mō te haerenga 240 km i te tere o te 20 km/h:
\[ t = \frac{s}{v} \]
\[ t = \frac{240 \, \text{km}}{20 \, \text{km/h}} \]
\[ t = 12 \, \text{jam} \]
Nō reira, ko te roa o te wā e hiahiatia ana e te tereina hei uhi i te haerenga katoa he 12 hāora.
#### Pātai 5: Te Whakataurite i ngā Tawhiti mā ngā Mea e Rua
Pātai:
E rua ngā waka, a A rāua ko B, e tere ana i te tere pumau o te 60 km/h me te 80 km/h. Mēnā ka tīmata rāua te neke i te wā kotahi mai i ngā pūwāhi rerekē, he aha te tawhiti i waenganui i a rāua i muri i te 2 hāora?
Otinga:
Waka A:
\[ v_A = 60 \, \text{km/h} \]
\[ t = 2 \, \text{jam} \]
\[ s_A = v_A \ngā wā t \]
\[ s_A = 60 \, \text{km/haora} \times 2 \, \text{haora} \]
\[ s_A = 120 \, \text{km} \]
Waka B:
\[ v_B = 80 \, \text{km/h} \]
\[ t = 2 \, \text{jam} \]
\[ s_B = v_B \ngā wā t \]
\[ s_B = 80 \, \text{km/haora} \times 2 \, \text{haora} \]
\[ s_B = 160 \, \text{km} \]
Te rerekētanga o te tawhiti i waenganui i ngā mea e rua:
\[ \Delta s = s_B – s_A \]
\[ \Delta s = 160 \, \text{km} – 120 \, \text{km} \]
\[ \Delta s = 40 \, \text{km} \]
Nō reira, i muri i ngā hāora e 2, ko te tawhiti i waenganui i ngā waka e rua he 40 km.
### Whakamutunga
Ko te Nekehanga Raina Taurite he ariā taketake i roto i te ahupūngao e whakaahua ana i te nekehanga i te tere pumau. Mā roto i ngā tauira kua whakaratohia, e tumanakohia ana kia mārama ake ngā kaipānui ki te whakamahi i te tauira nekehanga raina taurite taketake i roto i ngā āhuatanga rerekē. Ehara i te mea ka āwhina noa ēnei raruraru i te māramatanga ariā engari ka āwhina hoki i te whakamahinga mahi i roto i te oranga o ia rā. Hei mārama ake i te nekehanga raina taurite, e taunakihia ana kia haere tonu te whakaharatau me ngā momo raruraru.
