Ma'anar motsi na layi mara tsari
Motsin layi mara tsari shine motsi a cikin hanzari akai-akai. A wata ma'anar, motsi mara tsari mara tsari = motsi tare da girman hanzari akai-akai shine kuma alkiblar hanzari akai-akai. Alkiblar hanzari akai-akai = alkiblar gudu akai-akai = alkiblar motsawa akai-akai = alkiblar motsi akai-akai = alkiblar motsi akai-akai = abu yana motsawa a cikin layi madaidaiciya. Girman hanzari akai-akai yana nufin cewa girman gudu ko gudu yana ƙaruwa akai-akai.
Misali na farko:
Da farko abu yana hutawa. Bayan daƙiƙa ɗaya, abu yana motsawa a gudun m2/s. Bayan daƙiƙa biyu, abu yana motsawa a gudun m4/s. Bayan daƙiƙa uku, abu yana motsawa a gudun m6/s. Bayan daƙiƙa huɗu, abu yana motsawa a gudun m8/s. Da sauransu...
Kowace daƙiƙa 1, saurin abu yana ƙaruwa da m2/s. Abu yana fuskantar saurin gudu na m2/s a cikin daƙiƙa 1 ko m2/s a cikin daƙiƙa ko m2/s a cikin daƙiƙa 2.
Misali na biyu:
Abu yana fara motsawa da sauri na m 10/s. Bayan daƙiƙa ɗaya.
An rage gudu zuwa m9/s. Bayan daƙiƙa biyu, gudun yana raguwa zuwa m8/s. Bayan daƙiƙa uku, gudun yana raguwa zuwa m7/s. Bayan daƙiƙa huɗu, gudun yana raguwa zuwa m6/s. Haka kuma ... Kowace daƙiƙa 1, saurin abin yana raguwa da m1/s. Abin yana da raguwar gudu na m1/s a cikin daƙiƙa 1 ko m1/s a cikin daƙiƙa 1 ko m1/s a cikin daƙiƙa 2.
Daidaito na motsi na layi mara iri ɗaya
Akwai dabarun lissafi guda uku da ake amfani da su akai-akai:
v t = v o + a
d = v o t + 1⁄2 a 2
v t 2 = v o 2 + 2 talla
v o = saurin farko (mita/daƙiya), v t = gudun ƙarshe (mita/daƙiya), a = hanzari (mita/daƙiya murabba'i), t = tazara ta lokaci (daƙiya), d = nisa (mita).
Misalin matsala ta 1:
Kwayar cuta, da farko tana hutawa, sannan tana samun saurin gudu na m2/s 2 na tsawon daƙiƙa 10. Lissafa saurin ƙarshe na ƙwayar cuta.
Magani:
Ba tare da lissafi ba:
Hanzari (a) = 2 m/s 2 yana nufin ƙaruwar gudu (v) da 2 m/s a kowace daƙiƙa 1. Bayan daƙiƙa 2, v = 4 m/s. Bayan daƙiƙa 10, v = 20 m/s.
Amfani da lissafi:
Sananne: v o = 0 m/s (ƙwayar cuta a hutawa), a = 2 m/s 2 , t = 10 s
Ana so: v t
v t = v o + a = 0 + (2)(10) = 20 m/s
Misalin matsala ta 2:
Mota tana tafiya a kan hanya madaidaiciya a gudun kilomita 60/h. Domin akwai cikas, direban yana birki, don haka motar tana da raguwar gudu na mita 10/s2. Wane nisa motar ke tafiya har yanzu har sai ta tsaya bayan an gama birki?
Wanda aka sani:
v o = 60 km/h = 60 (1000 m)/3600 s = 17 m/s
v t = 0 m/s (tashoshin mota)
2a = – 10 m/s
Ana so: nisa (d)
Magani:
v t 2 = v o 2 + 2 talla
(0) 2 = (17) 2 + 2(-10) d
0 = 289 – 20 kwana
289 = 20 kwana
d = 289: 20 = mita 14.45
Misalin matsala ta 3:
Jadawalin da ke ƙasa jadawalin motsi ne na layi mara tsari, v yana wakiltar gudu, kuma t yana nuna lokaci. Girman hanzarin abubuwa bisa ga jadawalin shine ...
Misalin matsala ta 4:
Motsin mota yana samar da jadawalin gudu (v) da lokaci (t) kamar yadda aka nuna a hoton da ke gefe. Idan yankin da ke ƙarƙashin jadawalin (yankin da aka yi inuwa) ya kai mita 48, to saurin motar shine ...
Inuwa mai faɗi = jimlar nisa = mita 48
v o = 8 m/s, v t = 16 m/s, t = 1 m/s
v t = v o + a
16 = 8 + a (1)
a = 16 – 8
a = 8 m/s 2
or
Tambayoyi da amsoshi game da motsi na layi mara tsari
- Menene motsi na layi mara tsari?
Motsin layi mara tsari yana nufin motsin abu a kan layi madaidaiciya tare da saurin canzawa ko saurin gudu.
- Ta yaya ake wakiltar motsi mara tsari a kan jadawalin lokaci-lokaci na nesa?
Motsin layi mara tsari ana wakilta shi da layi mai lanƙwasa a kan jadawalin lokaci-lokaci na nesa.
- Wace rawa hanzari ke takawa a cikin motsi mara tsari na layi?
Saurin gudu muhimmin abu ne a cikin motsi mara tsari na layi. Shi ne saurin da saurin gudu ke canzawa akan lokaci.
- Ta yaya mutum zai iya gano motsi mara tsari akan jadawalin lokacin gudu?
Ana wakiltar motsi mara tsari ta hanyar layi mara daidaituwa (ƙaruwa ko raguwa) akan jadawalin lokacin gudu, wanda ke nuna cewa saurin yana canzawa akan lokaci.
- Menene ma'aunin hanzari a cikin Tsarin Raka'o'in Ƙasashen Duniya (SI)?
Naúrar hanzari a cikin tsarin SI shine mita a kowace daƙiƙa murabba'i (m/s²).
- Menene dabarar motsi a cikin motsi mara tsari na layi, idan aka yi la'akari da saurin farko, hanzari, da lokaci?
Tsarin shine s = ut + ½at², inda s shine motsi, u shine saurin farko, a shine hanzari, kuma t shine lokaci.
- Shin matsugunin 's' zai iya zama mara kyau a cikin motsi mara tsari?
Eh, 's' na iya zama mara kyau a cikin motsi mara tsari na layi. Wannan zai nuna motsi a akasin alkiblar da aka zaɓa mai kyau.
- Shin zai yiwu wani abu a cikin motsi mara tsari ya tsaya?
Eh, abu a cikin motsi mara tsari na layi zai iya tsayawa idan saurinsa ya yi aiki akasin alkiblar motsi kuma ya rage saurin abu zuwa sifili sosai.
- Menene dabarar gudun ƙarshe a cikin motsi mara tsari, idan aka yi la'akari da saurin farko, hanzari, da lokaci?
Tsarin shine v = u + a, inda v shine saurin ƙarshe, u shine saurin farko, a shine hanzari, kuma t shine lokaci.
- Ta yaya manufar jerk ta shafi motsi mara tsari na layi?
Jerk shine saurin canjin hanzari. A cikin motsi mara tsari, idan hanzarin ba ya canzawa kuma yana canzawa akan lokaci, to akwai jerk.
