This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Haya, tutatumia uchambuzi wa vipimo (dimensional analysis) kuangalia usahihi wa fomula hizi. a) v^2 = u^2 + 2as ambapo u na v ni kasi, a ni mchapuko, na s ni umbali. Step 1: Pata vipimo vya kila kigezo. • Vipimo vya kasi (v au u): [L T^-1] • Vipimo vya mchapuko (a): [L T^-2] • Vipimo vya umbali (s): [L] Step 2: Pata vipimo vya kila neno katika fomula. • Vipimo vya v^2: [v^2] = ([L T^-1])^2 = [L^2 T^-2] • Vipimo vya u^2: [u^2] = ([L T^-1])^2 = [L^2 T^-2] • Vipimo vya 2as: (Namba 2 haina vipimo) [2as] = [a][s] = [L T^-2][L] = [L^2 T^-2] Step 3: Linganisha vipimo vya maneno yote. Kwa kuwa vipimo vya kila neno ([L^2 T^-2]) ni sawa, fomula hii ni sahihi kwa mujibu wa uchambuzi wa vipimo. Fomula ni sahihi b) E = mc^2 ambapo E ni nishati, m ni masi, na c ni kasi ya mwanga. Step 1: Pata vipimo vya kila kigezo. • Vipimo vya nishati (E): Nishati ina vipimo sawa na kazi (force × distance) au kinetic energy ((1)/(2)mv^2). [E] = [M][L T^-1]^2 = [M L^2 T^-2] • Vipimo vya masi (m): [M] • Vipimo vya kasi ya mwanga (c): [L T^-1] Step 2: Pata vipimo vya upande wa kulia wa fomula. • Vipimo vya mc^2: mc^2] = [m][c]^2 = [M^2 = [M L^2 T^-2] Step 3: Linganisha vipimo vya pande zote mbili. Kwa kuwa vipimo vya upande wa kushoto ([M L^2 T^-2]) ni sawa na vipimo vya upande wa kulia ([M L^2 T^-2]), fomula hii ni sahihi kwa mujibu wa uchambuzi wa vipimo. Fomula ni sahihi c) T = 2 ambapo T ni kipindi. Step 1: Pata vipimo vya kila kigezo. • Vipimo vya kipindi (T): [T] • 2 ni namba isiyo na vipimo (dimensionless constant). Step 2: Linganisha vipimo vya pande zote mbili. Upande wa kushoto una vipimo vya muda ([T]), lakini upande wa kulia hauna vipimo. Hii inamaanisha pande hizo mbili hazilingani kimipimo. Fomula si sahihi That's 2 down. 3 left today — send the next one.