Question

Um carro movimenta-se segundo a função horário V=20+2t (no SI). A)Qual  a velocidade inicial do carro? b)Qual a velocidade do carro no instante de 15s? c)Em que instante o carro adquire a velocidade de 60m/s?​.

Answer 1

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⠀⠀⠀☞ a) v₀ = 20 [m/s]; b) v(15) = 50 [m/s]; c) t = 20 [s]. ✅

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⠀⠀⠀⭐⠀Para realizar este exercício vamos rever a estrutura da função horária da velocidade.⠀⭐⠀

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⠀⠀⠀☔⠀Partindo da relação da aceleração média temos a função horária da velocidade:

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                        $\large\gray{\boxed{~~\begin{array}{lcr}&&\\&\Large\pink{\underline{\bf~~~~Func_{\!\!,}\tilde{a}o~hor\acute{a}ria~~~~}}&\\&\Large\pink{\underline{\bf~~~~da~velocidade~~~~}}&\\\\\\\\&\green{\sf\clubsuit~~\underline{~Rearranjando~a_m:~}~~\clubsuit}&\\\\&\orange{\sf a_m = \dfrac{\Delta v}{\Delta t} = \dfrac{v_f - v_i}{t_f - t_i}}&\\\\\\&\green{\sf\spadesuit~~\underline{~Assumindo~t_i = 0~[s]:~}~~\spadesuit}&\\\\&\orange{\sf a_m = \dfrac{v_f - v_i}{t}}&\\\\&\orange{\sf a_m \cdot t = v_f - v_i}&\\\\&\orange{\sf v_f = v_i + a_m \cdot t}&\\\\\\&\green{\sf\clubsuit~~\underline{~Sendo~v_f~uma~func_{\!\!,}\tilde{a}o~de~t:~}~~\clubsuit}&\\\\\\&\Large\red{\boxed{\pink{\boxed{\begin{array}{lcr}\green{\star}&&\green{\star}\\&\!\!\orange{\bf V(t) = V_0 + a_m \cdot t}\!\!&\\\green{\star}&&\green{\star}\\\end{array}}}}}&\\&&\\&&\end{array}~~}}$

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⠀⠀⠀➡️⠀Desta forma temos:

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                                  $\quad\LARGE\gray{\boxed{\sf\blue{~~v(t) = \orange{\overbrace{\blue{20}}^{= V_{\footnotesize 0}}} + \orange{\overbrace{\blue{2}}^{= a}} \cdot t~~}}}$

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a) v₀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀✍

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                                   $\huge\green{\boxed{\rm~~~\gray{v_0}~\pink{=}~\blue{ 20~[m/s] }~~~}}$ ✅  

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b) v(15)⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀✍

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$\LARGE\blue{\sf v(15) = 20 + 2 \cdot 15}$

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$\LARGE\blue{\sf v(15) = 20 + 30}$

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                              $\huge\green{\boxed{\rm~~~\gray{v(15)}~\pink{=}~\blue{ 50~[m/s] }~~~}}$ ✅

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c) v = 60⠀⠀⠀⠀⠀⠀⠀ ⠀⠀✍

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$\LARGE\blue{\sf 60 = 20 + 2 \cdot t}$

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$\LARGE\blue{\sf 60 - 20 = 2 \cdot t}$

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$\LARGE\blue{\sf 40 = 2 \cdot t}$

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$\LARGE\blue{\sf t = \dfrac{40}{2}}$

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                                        $\qquad\huge\green{\boxed{\rm~~~\gray{t}~\pink{=}~\blue{ 20~[s] }~~~}}$ ✅  

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                             $\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

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⠀⠀☀️ L͎̙͖͉̥̳͖̭̟͊̀̏͒͑̓͊͗̋̈́ͅeia mais sobre funções horárias:

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                                     https://brainly.com.br/tarefa/48564462 ✈  

                                     https://brainly.com.br/tarefa/38431619 ✈  

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                                     $\huge\blue{\text{\bf\quad Bons~estudos.}}$ ☕

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                                          $\quad\qquad(\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios})$ ☄

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                             $\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }\LaTeX}$✍

                                $\sf(\purple{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly}$ ☘☀❄☃☂☻)

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                                                          $\Huge\green{\text{ \underline{\red{\mathbb{S}}\blue{\mathfrak{oli}}~}~\underline{\red{\mathbb{D}}\blue{\mathfrak{eo}}~}~\underline{\red{\mathbb{G}}\blue{\mathfrak{loria}}~} }}$ ✞

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