Labari game da Adadin kimiyyar lissafi a cikin motsi na layi
1. Tazarar lokaci
Idan abu ya motsa daga wani wuri zuwa wani, abu yana buƙatar takamaiman tazara. Alamar lokaci ita ce t (lokaci). Sashen tsarin duniya na lokaci shine second(s).
2. Nisa da ƙaura
Nisa ita ce tsawon hanyar da abu ya ɗauka. Nisa adadi ne na sikelin, inda adadin bai dogara da alkibla ba. Alamar nisan ita ce d kuma sashin tsarin ƙasa da ƙasa mita ne (m).
Komawa wani canji ne a matsayin abu. Komawa wani adadi ne na vector, don haka komawa ya ƙunshi girman komawa da alkiblar komawa. Komawa ya dogara da alkiblar don haka zai iya zama mai kyau ko mara kyau. Idan an ƙididdige shi a cikin daidaitattun Cartesian to bisa ga yarjejeniyar, idan alkiblar komawa tana kan alkiblar x mai kyau da kuma alkiblar y mai kyau, to komawa ta tabbata. Akasin haka, idan alkiblar komawa tana kan alkiblar x mai kyau da kuma alkiblar y mai kyau to komawa ta cancanci. Alkiblar komawa kuma ana yawan faɗinta a arewa, gabas, kudu, yamma. Alamar komawa ita ce d kuma sashin tsarin ƙasa da ƙasa mita ne (m).
Misalin matsala ta 1:
Ɗalibi yana tafiya zuwa gabas har zuwa mita 2. Menene nisan da kuma girman gudun hijirar ɗalibin?
a = matsayin farko, b = matsayin ƙarshe.
Nisa (d) = mita 2
Girman gudun hijira (d) = mita 2. Alkiblar gudun hijira = gabas
Misalin matsala ta 2:
Ɗalibi yana tafiya gabas har zuwa mita 2 sannan ya nufi yamma har zuwa mita 2. Menene nisan da girman ƙaurar ɗalibin?
a = matsayin farawa da matsayin ƙarshe
Nisa (d) = mita 2 + mita 2 = mita 4
Girman ƙaura (d) = 2 m – 2 m = 0. Matsayin ƙarshe = matsayin farko don kada a sami sauyawa.
Misalin matsala ta 3:
Ɗalibi yana tafiya gabas har zuwa mita 2 sannan ya nufi yamma har zuwa mita 1. Menene nisan da girman ƙaurar ɗalibin?
a = matsayin farawa, b = matsayin ƙarshe.
Nisa (d) = mita 2 + mita 1 = mita 3
Girman gudun hijira (d) = 2 m – 1 m = 1 m. Alkiblar gudun hijira = gabas
3. Sauri da gudu
Sauri adadi ne na sikelin, yayin da gudu kuma adadi ne na vector. Sauri ya ƙunshi girman gudu da alkiblar gudu. Alamar gudu ita ce v kuma alamar gudu ita ce v (gudu). Sashen tsarin duniya na gudu da gudu shine mita a kowace daƙiƙa (m/s).
a. Matsakaicin gudu da matsakaicin gudu
Misalin matsala ta 1:
Ɗalibi yana tafiya zuwa gabas har zuwa mita 2 na daƙiƙa 1. Menene matsakaicin gudu da girman matsakaicin gudu na ɗalibi?
Alkiblar matsakaicin saurin gudu = alkiblar ƙaura = zuwa gabas
Misalin matsala ta 2:
Ɗalibi yana tafiya zuwa gabas har zuwa mita 2 na daƙiƙa 1 sannan ya yi tafiya zuwa yamma har zuwa mita 1 na daƙiƙa 2. Menene matsakaicin gudu da girman matsakaicin gudu na ɗalibi?
Alkiblar matsakaicin gudu = alkiblar ƙaura = zuwa gabas
b. Saurin gaggawa da saurin gaggawa
Gudu nan take = ɗan nisa da aka yi a cikin ɗan gajeren lokaci. Girman gudun nan take = ƙaramin gudun da aka yi a cikin ɗan gajeren lokaci. Idan ka taɓa hawa babur ko mota, tabbas ka ga na'urar auna gudu. Lokacin hawa babur, saurin babur yana canzawa kuma na'urar auna gudu tana nuna shi.
A fannin kimiyyar lissafi, saurin gaggawa sau da yawa ana rage shi da sauri. Haka nan, saurin gaggawa sau da yawa ana rage shi da sauri. Lura cewa za mu iya maye gurbin girman saurin da sauri. Wannan saboda girman saurin ana ɗaukarsa daidai yake da sauri. Ana ɗaukar girman saurin daidai yake da sauri saboda nisa da girman motsi iri ɗaya ne idan ya yi ƙanƙanta sosai. Kodayake nisan da girman ƙaura ba koyaushe suke iri ɗaya ba (idan aka kwatanta da tattaunawar game da nisa da ƙaura), amma idan nisan da girman ƙaura sun yi ƙanƙanta sosai to dole ne su sami ƙima iri ɗaya.
4. Hanzartawa
Hawan gaggawa adadi ne na vector don haka akwai girman hanzari da alkiblar hanzari. Alamar hawan gaggawa ita ce (hawan gaggawa). Sashin SI na hawan gaggawa mita ne a kowace daƙiƙa murabba'i (m/s 2 ).
a. Matsakaicin hanzari
Matsalar samfurin:
Mota tana fara tafiya gabas daga hutu har sai ta kai gudun mita 10/s na tsawon daƙiƙa 5. A ƙididdige girman matsakaicin saurin gudu!
Alkiblar matsakaicin saurin gudu tana gabas.
A matsakaici, saurin motar yana ƙaruwa da mita 2/s a kowace daƙiƙa. Idan girman saurin motar ya kasance mai daidaito to saurin motar koyaushe yana ƙaruwa da mita 2/s a kowace daƙiƙa. Idan girman saurin motar bai daidaita ba to saurin motar ba koyaushe yake ƙaruwa da mita 2/s a kowace daƙiƙa ba. Wataƙila saurin motar ya ƙaru da mita 1/s a daƙiƙa ta farko, sannan ta hanyar ƙara mita 3/s a daƙiƙa ta biyu. Amma a matsakaici, lokacin da ake motsi na daƙiƙa 5, girman saurin motar yana ƙaruwa da mita 2/s a kowace daƙiƙa.
b. Haɓakawa nan take
Haɓaka gaggawa sau da yawa canji ne a cikin sauri a cikin ɗan gajeren lokaci. Haɓaka gaggawa sau da yawa ana kiransa da haɓaka gaggawa. Saboda haka idan aka ce haɓaka gaggawa, abin da ake nufi shine haɓaka gaggawa. Ana cewa abu yana fuskantar haɓaka idan saurinsa ya canza. Haɓaka kuma adadi ne na vector, wanda ya haɗa da girman saurin da alkiblar saurin. Saboda haka akwai yanayi uku da ake cewa abu mai motsi yana hanzartawa. Na farko, ana cewa abu yana fuskantar haɓaka idan girman gudun ko saurin ya canza (alkiblar saurin yana dawwama).
A misali na farko, mota tana hutawa da farko (v = 0). Bayan daƙiƙa ɗaya, saurinta ya ƙaru zuwa 5 m/s. Saurin motar ya ƙaru don haka ana cewa motar tana gudu. A misali na biyu, mota tana motsawa da farko da 5 m/s. Daƙiƙa ɗaya sai motar ta tsaya. Saurin motar ya ragu saboda ana cewa motar tana fuskantar saurin da ba shi da kyau ko kuma motar tana fuskantar raguwar gudu. Na biyu, ana cewa abu yana fuskantar saurin gudu idan alkiblar saurinsa ta canza (girman gudu ko saurin yana dawwama). Alkiblar gudu = alkiblar ƙaura = alkiblar motsi. Na uku, ana cewa abu yana fuskantar saurin gudu idan girman da alkiblar saurinsa suka canza.
