Question

A) os móveis se movimentam no mesmo sentido ou em sentido contrários?

B) em que instante é em que Pontos móveis se encontram?

C) determine a velocidade de cada móvel.




MIM AJUDA PFV!!!!!​

Answer 1

$\mathrm{Analisando\ as\ retas\ A\ e\ B\ no\ gr\acute{a}fico}\ s\times t\ \mathrm{\acute{e}\ poss\acute{\i}vel}\\ \mathrm{identificar\ alguns\ pontos}\text{.}$

$\mathrm{A}\Longrightarrow (0,0)\ \text{e}\ (10,100)$

$\mathrm{B}\Longrightarrow (0,150)\ \text{e}\ (30,0)$

$\mathrm{Desse\ modo},\ \text{pode-se}\ \mathrm{determinar\ as\ fun\c{c}\tilde{o}es\ hor\acute{a}rias}\\ \mathrm{de\ A\ e\ B.}$

$\mathrm{Para\ A}\text{:}$

$s_A(t)=mt+n$

$\Longrightarrow m=\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{100-0}{10-0}\ \therefore\ m=10$

$s_A(0)=0\Longrightarrow 10(0)+n=0\ \therefore\ n=0$

$\Longrightarrow \boxed{s_A(t)=10t}$

$\mathrm{Para\ B}\text{:}$

$s_B(t)=pt+q$

$\Longrightarrow p=\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{0-150}{30-0}\ \therefore\ p=-5$

$s_B(0)=150\Longrightarrow -5(0)+q=150\ \therefore\ q=150$

$\Longrightarrow \boxed{s_B(t)=150-5t}$

$\mathbf{a)}\ \mathrm{Os\ m\acute{o}veis\ se\ movimentam\ em\ sentidos\ contr\acute{a}rios,}\\ \mathrm{pois\ o\ gr\acute{a}fico\ de\ A\ \acute{e}\ crescente\ e\ o\ de\ B\ \acute{e}\ decrescente.}$

$\mathbf{b)}\ \mathrm{O\ instante\ em\ que\ os\ m\acute{o}veis\ se\ encontram\ \acute{e}}\text{:}$

$s_A(t)=s_B(t)\Longrightarrow 10t=150-5t\ \therefore\ \boxed{t=10\ \text{s}}$

$\mathbf{c)}\ \mathrm{A\ velocidade\ de\ cada\ m\acute{o}vel\ ser\acute{a},\ respectivamente}\text{:}$

$v_A=\dfrac{\mathrm{d}s_A}{\mathrm{d}t}=\dfrac{\mathrm{d}}{\mathrm{d}t}(10t)\ \therefore\ \boxed{v_A=10\ \mathrm{m/s}}$

$v_B=\dfrac{\mathrm{d}s_B}{\mathrm{d}t}=\dfrac{\mathrm{d}}{\mathrm{d}t}(150-5t)\ \therefore\ \boxed{v_B=-5\ \mathrm{m/s}}$