Question

body travel a distance 10 kilometre with a speed of 30 kilometre -1 and the and then the next 40 kmto 50 kilometre per hour-1 find
the average speed for a whole journey
​

Answer 1

Given :

• Body travel a distance ${\sf s_1=10\:km }$ with speed ${\sf v_1=30\: km/h}$
• It covers next Distance in ${\sf s_2=40 \: km/h }$ with speed ${\sf v_2=50 \; km/h}$

To Find :

• Average Speed ${\sf (v_{av})}$

Formula Used :

$\implies\underline{\boxed{\sf Average \: Speed (v_{av})=\dfrac{Total \: Distance }{Total \; Time}}}$

Solution :

➩ Total Time (T) -

$\implies\boxed{\sf Time = \dfrac{Distance}{Speed} }$

$\implies{\sf t_1=\dfrac{s_1}{v_1} }$

$\implies{\sf t_1=\dfrac{10}{30} }$

$\implies{\bf t_1=\dfrac{1}{3}\:h}$

$\implies{\sf t_2=\dfrac{s_2}{v_2} }$

$\implies{\sf t_2=\dfrac{40}{50}}$

$\implies{\bf t_2=\dfrac{4}{5}\: h}$

$\implies{\sf T = t_1 + t_2}$

$\implies{\sf T = \dfrac{1}{3}+\dfrac{4}{5}}$

$\implies{\bf T = \dfrac{17}{15}\: h}$

__________________________________

$\implies{\sf V_{av}=\dfrac{s_1+s_2}{T} }$

$\implies{\sf \dfrac{10+40}{\dfrac{17}{15}}}$

$\implies{\sf 50 \times \dfrac{15}{17} }$

$\implies{\sf \dfrac{750}{17}}$

$\implies{\bf V_{av}=44.11 \: km/h }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀OR

$\implies{\sf v_{av}=44.11 \times \dfrac{5}{18} }$

$\implies{\bf v_{av}=12.2\: m/s}$

Answer

Average speed of journey is ${\bf 44.11 \: km/h \: or \; 12.2 \: m/s}$