Question

Um automóvel faz metade de um percurso com velocidade média

de 40 km/h e a outra metade com velocidade média de 60 km/h. Qual

a velocidade média do automóvel no percurso todo? a)16 km/h b)48 km/h c)64 km/h d)24 km/h e)32 km/h

!COM A CONTA POR FAVOR!​

Answer 1

Resposta:

Letra B.

Explicação passo-a-passo:

$v_1=40\ \dfrac{km}{h};\ s_1=\dfrac{x}{2}\\\\ v_2=60\ \dfrac{km}{h};\ s_2=\dfrac{x}{2}\\\\ v_1=\dfrac{s_1}{t_1}\ \therefore\ 40=\dfrac{x}{2}\bigg(\dfrac{1}{t_1}\bigg)\ \therefore\ \boxed{t_1=\dfrac{x}{80}}\\\\ v_2=\dfrac{s_2}{t_2}\ \therefore\ 60=\dfrac{x}{2}\bigg(\dfrac{1}{t_2}\bigg)\ \therefore\ \boxed{t_2=\dfrac{x}{120}}$

$\boxed{t_{total}=t_1+t_2}=\dfrac{x}{80}+\dfrac{x}{120}\ \therefore\ \boxed{t_{total}=\dfrac{x}{48}}\\\\ \boxed{s_{total}=s_1+s_2}=\dfrac{x}{2}+\dfrac{x}{2}\ \therefore\ \boxed{s_{total}=x}\\\\ \boxed{v_m=\dfrac{s_{total}}{t_{total}}}=\dfrac{x}{\dfrac{x}{48}}=\dfrac{48x}{x}\ \therefore\ \boxed{v_m=48\ \dfrac{km}{h}}$