Question

1) Um móvel dotado de movimento uniforme, percorre a distância de 10800 m em duas horas. Qual é a sua velocidade em km / h?

2) Calcular em segundos o tempo gasto por um carro para percorrer 180 km numa velocidade media de 60 km / h,

3) Calcular em minutos o tempo gasto por um avião para percorrer 230 km, nume velocidade de 115 km / h.

4) Quantos km percorreu um avião que viajou 18.000 segundos numa velocidade de 250 km / h. preciso das respostas ainda hoje.

Answer 1

$\large\begin{array}{l} \textsf{1)}\\\\ \bullet~~\textsf{Dist\^ancia percorrida:}\\\\ \mathsf{d=10\,800~m}\\\\ \mathsf{d=10,\!8\cdot (1\,000~m)}\qquad\quad\textsf{(mas }\mathsf{1\,000~m=1~km}\textsf{)}\\\\ \mathsf{d=10,\!8~km;} \end{array}$


$\large\begin{array}{l} \bullet~~\textsf{Tempo de percurso: }\mathsf{\Delta t=2~h.}\\\\\\ \textsf{O m\'ovel est\'a em movimento uniforme, logo possui velocidade}\\\textsf{constante, que \'e dada por}\\\\ \mathsf{v=\dfrac{d}{\Delta t}}\\\\ \mathsf{v=\dfrac{10,\!8~km}{2~h}}\\\\ \mathsf{v=\dfrac{10,\!8}{2}~\dfrac{km}{h}}\\\\ \boxed{\begin{array}{c}\mathsf{v=5,\!4~km/h} \end{array}} \end{array}$

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$\large\begin{array}{l} \textsf{2)}\\\\ \bullet~~\textsf{Dist\^ancia percorrida: }\mathsf{180~km;}\\\\ \bullet~~\textsf{Velocidade m\'edia: }\mathsf{v=60~km/h;}\\\\ \bullet~~\textsf{Tempo de percurso: }\mathsf{\Delta t.} \end{array}$


$\large\begin{array}{l} \textsf{Temos que}\\\\ \mathsf{v=\dfrac{d}{\Delta t}}\\\\ \mathsf{v\cdot \Delta t=d}\\\\ \mathsf{\Delta t=\dfrac{d}{v}}\\\\ \mathsf{\Delta t=\dfrac{180~km}{60~\frac{km}{h}}}\\\\ \mathsf{\Delta t=\dfrac{180}{60}~h}\\\\ \mathsf{\Delta t=3~h\qquad\quad(\textsf{mas }}\mathsf{1~h=3\,600~s}\textsf{)} \end{array}$

$\large\begin{array}{l} \mathsf{\Delta t=3\cdot (3\,600~s)}\\\\ \boxed{\begin{array}{c}\mathsf{\Delta t=10\,800~s} \end{array}} \end{array}$

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$\large\begin{array}{l} \textsf{3)}\\\\ \bullet~~\textsf{Dist\^ancia percorrida: }\mathsf{d=230~km};\\\\ \bullet~~\textsf{Velocidade m\'edia: }\mathsf{v=115~km/h};\\\\ \bullet~~\textsf{Tempo de percurso: }\mathsf{\Delta t.} \end{array}$


$\large\begin{array}{l} \textsf{Novamente, temos}\\\\ \mathsf{v=\dfrac{d}{\Delta t}}\\\\ \mathsf{\Delta t=\dfrac{d}{v}}\\\\ \mathsf{\Delta t=\dfrac{230~km}{115~\frac{km}{h}}}\\\\ \mathsf{\Delta t=\dfrac{230}{115}~h} \end{array}$

$\large\begin{array}{l} \mathsf{\Delta t=2h}\qquad\quad\textsf{(mas }\mathsf{1~h=60~min}\textsf{)}\\\\ \mathsf{\Delta t=2\cdot (60~min)}\\\\ \boxed{\begin{array}{c}\mathsf{\Delta t=120~min} \end{array}} \end{array}$

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$\large\begin{array}{l}\textsf{4)}\\\\ \bullet~~\textsf{Tempo de percurso: }\mathsf{\Delta t=18\,000~s}\\\\ \mathsf{\Delta t=5\cdot (3\,600~s)}\qquad\quad\textsf{(mas }\mathsf{3\,600~s=1~h}\textsf{)}\\\\ \mathsf{\Delta t=5~h;}\\\\\\ \bullet~~\textsf{Velocidade m\'edia: }\mathsf{v=250~km/h;}\\\\ \bullet~~\textsf{Dist\^ancia percorrida: }\mathsf{d.} \end{array}$


$\large\begin{array}{l}\textsf{Segue,}\\\\ \mathsf{v=\dfrac{d}{\Delta t}}\\\\ \mathsf{d=v\cdot \Delta t}\\\\ \mathsf{d=(250~\frac{km}{h})\cdot (5~h)}\\\\ \boxed{\begin{array}{c}\mathsf{d=1\,250~km} \end{array}} \end{array}$


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$\large\textsf{Bons estudos! :-)}$


Tags: velocidade média tempo distância conversão unidade de medida cinemática