# Misalan Tambayoyin Motsi Mai Layi Mai Iri ɗaya
Motsin Layi na Uniform Linear (GLB) muhimmin ra'ayi ne a fannin kimiyyar lissafi. Shi ne motsin abu a kan hanya madaidaiciya a cikin gudu mai ɗorewa. Wannan yana nufin babu hanzari, kuma saurin yana nan a ko'ina. Wannan labarin zai samar da misalai da yawa na matsalolin GLB da mafita don taimaka muku fahimtar wannan ra'ayi sosai.
## Ma'anar Asali ta GLB
Kafin mu shiga cikin tambayoyin misalai, bari mu fara sake duba wasu muhimman ra'ayoyi na Motsin Layi na Uniform. A cikin Motsin Layi na Uniform, ana bayyana lissafin saurin kamar haka:
\[ v = \frac{s}{t} \]
Ina:
– \( v \) shine gudun,
– \(s \) shine nisa,
– \( t \) lokaci ne.
Tunda gudun ba ya canzawa, ana iya kwatanta nisan da aka yi tafiya da shi ta hanyar lissafi mai layi:
\[s = v \times t \]
tare da:
– \(s \) shine nisan da aka yi tafiya,
– \( v \) shine saurin da ba ya canzawa,
– \( t \) shine lokacin da ake buƙata.
### Misali Tambayoyi da Tattaunawa
#### Tambaya ta 1: Lissafin Nisa
Tambaya:
Mota tana tafiya a gudun kilomita 60/h na tsawon awanni 2. Har yaushe motar take tafiya?
Mafita:
Amfani da dabarar nisa ta asali a cikin GLB, \( s = v \times t \):
– Gudun (\( v \)) = kilomita 60/h
– Lokaci (\( t \)) = awanni 2
Nisa da aka yi tafiya (\( s \)):
\[s = v \times t \]
\[s = 60 \, \text{km/awa} \sau 2 \, \text{awanni} \]
\[s = 120 \, \rubutu{km} \]
Don haka, nisan da motar ta yi tafiya shine kilomita 120.
#### Tambaya ta 2: Lissafin Lokaci
Tambaya:
Mai tafiya a ƙasa yana tafiya a kan gudun da ba ya canzawa na kilomita 5/h. Idan dole ne ya yi tafiyar kilomita 15, tsawon lokacin da zai ɗauka?
Mafita:
Amfani da dabarar asali don lokaci a cikin GLB, \( t = \frac{s}{v} \):
– Nisa (\( s \)) = 15 km
– Gudun (\( v \)) = kilomita 5/h
Lokacin da ake buƙata (\( t \)):
\[t = \frac{s}{v} \]
\[ t = \frac{15 \, \text{km}}{5 \, \text{km/h}} \]
\[t = 3 \, \text{jam} \]
Don haka, lokacin da mai tafiya a ƙasa ke buƙata shine awanni 3.
#### Tambaya ta 3: Lissafin Sauri
Tambaya:
Mai keke yana tafiya kilomita 18 cikin awanni 1.5. Menene gudun da mai keke ke yi akai-akai?
Mafita:
Amfani da dabarar asali don saurin gudu a cikin GLB, \( v = \frac{s}{t} \):
– Nisa (\( s \)) = 18 km
– Lokaci (\( t \)) = awanni 1.5
Sauri (\( v \)):
\[ v = \frac{s}{t} \]
\[ v = \frac{18 \, \text{km}}{1.5 \, \text{hour}} \]
\[ v = 12 \, \rubutu{km/h} \]
Don haka, gudun da babur ke yi akai-akai shine kilomita 12/h.
#### Tambaya ta 4: Haɗakar Nisa da Lokaci
Tambaya:
Jirgin ƙasa yana tafiya kilomita 240 a cikin gudu mai daidaito. Idan ya ɗauki awanni 3 kafin ya cika kwata na farko na nisan, a ƙididdige jimlar lokacin da ake buƙata don kammala dukkan tafiyar.
Mafita:
Da farko, muna ƙididdige nisan kwata (1/4) na jimlar tafiyar:
\[ s_1 = \frac{1}{4} \times 240 \, \text{km} \]
\[ s_1 = 60 \, \text{km} \]
Jirgin yana tafiyar kilomita 60 cikin awanni 3. Don haka, saurin jirgin:
\[ v = \frac{60 \, \text{km}}{3 \, \text{hour}} \]
\[ v = 20 \, \rubutu{km/h} \]
Na gaba, za mu ƙididdige jimillar lokacin tafiyar kilomita 240 a gudun kilomita 20/h:
\[t = \frac{s}{v} \]
\[ t = \frac{240 \, \text{km}}{20 \, \text{km/h}} \]
\[t = 12 \, \text{jam} \]
Don haka, jimillar lokacin da jirgin zai ɗauka don ya yi tafiya gaba ɗaya shine awanni 12.
#### Tambaya ta 5: Kwatanta Nisa ta Abubuwa Biyu
Tambaya:
Motoci biyu, A da B, suna tafiya a gudun kilomita 60/h da kuma kilomita 80/h bi da bi. Idan suka fara tafiya a lokaci guda daga wurare daban-daban, menene tazarar da ke tsakaninsu bayan awanni 2?
Mafita:
Mota A:
\[ v_A = 60 \, \text{km/h} \]
\[t = 2 \, \text{jam} \]
\[ s_A = v_A \times t \]
\[ s_A = 60 \, \text{km/awa} \sau 2 \, \text{awanni} \]
\[ s_A = 120 \, \rubutu{km} \]
Mota B:
\[ v_B = 80 \, \text{km/h} \]
\[t = 2 \, \text{jam} \]
\[ s_B = v_B \times t \]
\[ s_B = 80 \, \text{km/awa} \sau 2 \, \text{awanni} \]
\[ s_B = 160 \, \rubutu{km} \]
Bambancin nisa tsakanin su biyun:
\[ \Delta s = s_B – s_A \]
\[ \Delta s = 160 \, \text{km} – 120 \, \text{km} \]
\[ \Delta s = 40 \, \text{km} \]
Don haka, bayan awanni 2, nisan da ke tsakanin motocin biyu ya kai kilomita 40.
### Kammalawa
Motsin Layi Mai Daidaito (Uniform Linear Motion) wani muhimmin ra'ayi ne a fannin kimiyyar lissafi wanda ke bayyana motsi a cikin gudu mai daidaito. Ta hanyar misalan da aka bayar, ana sa ran masu karatu su fahimci yadda ake amfani da dabarar motsi mai daidaito a cikin yanayi daban-daban. Waɗannan matsalolin ba wai kawai suna taimakawa fahimtar ka'idoji ba ne, har ma da aikace-aikacen aiki a rayuwar yau da kullun. Don ƙarin fahimtar motsi mai daidaito, ana ba da shawarar ci gaba da yin aiki tare da matsaloli daban-daban.
