Question

Un mobil isi mareste viteza de la V1 = 36 km/h la V2 - 30m/s intr-un timp t = 1 min.
Sa se determine:
a) acceleratia
b) spatiul parcurs
c) viteza la jumatatea distentei
d) timpul in care ajunge la jumatatea distantei
e) spatiul strabatut in a doua secunda
PS: La punctul e) se cere spatiul strabatut in A DOUA secunda, nu in doua secunde
Multumesc!

Answer 1

[tex]\displaystyle\text{Se da:}\\ \\ v_0=36\frac{km}{h}=10\frac ms\\ \\ v=30\frac ms\\ \\ t=1min=60s\\ \\ a)a=?\frac{m}{s^2}\\ \\ b)d=?m\\ \\ c)d_1=\frac d2,\text{ }v_1=?\frac ms\\ \\ d)t_1=?s\\ \\ e)t_2=2s,\text{ }d_2=?m\\ \\ \\[/tex]


[tex]\displaystyle \text{Formule:}\\ \\ a)a=\frac{\Delta v}{t}\\ \\ a=\frac{v-v_0}{t}\\ \\ \\ b)d=\frac{(v+v_0)\times t}{2},\text{ aria graficului}\\ \\ \\ c)v_1^2=v_0^2+2\times d_1\times a, \text{ formula lui Galilei}\\ \\ v_1=\sqrt{v_0^2+d\times a}\\ \\[/tex]


[tex]\displaystyle d)d_1=\frac{(v_1+v_0)\times t}{2}\\ \\ t=\frac{d}{v_1+v_0}\\ \\ \\ e)\text{Trebuie sa aflam cit a parcurs intr-o secunda, anume a 2-a}\\ \\ \text{Deci formula:}\\ \\ d_2=v_{0_2}\times t_0+\frac{a\times t_0^2}{2}\\ \\ \text{Se transform in formula:}\\ \\ d_2=v_{0_2}+\frac a2\\ \\ \text{Unde }v_{0_2} \text{, reprezinta viteza pina la secunda } t_2\\ \\ \\[/tex]


[tex]\displaystyle v_{0_2}=v_0+a\times t_2\\ \\ \\ d_2=v_0+a\times t_2+\frac a2\\ \\ d_2=v_0+a\times (t_2+0,5)\\ \\ \\ \text{Se putea exprima prin diferenta dintre distanta 3 si 2}\\ \\ \text{Dar deloc numi place aceasta metoda}\\ \\ \\ \text{Calcule:}\\ \\ a)a=\frac{30-10}{60}=\frac 13\frac m{s^2}\\ \\ b)d=\frac{(30+10)\times 60}{2}=1200m\\ \\ c)v_1=\sqrt{10^2+1200\times \frac 13}\approx 22,36\frac ms\\ \\ d)t_1=\frac{1200}{10+22,36}=37,08s\\ \\ e)d_2=10+\frac 13\times(2+0,5)\approx 10,83m [/tex]