Question

A car travels for 4 hrs.Fir first 3 hours its goes away from the city A to city B its velocity is v1 and v2 for equal interval of time .In last 1 hr.it returns back with with velocity v3 and stops at some place between city A and city B . Find the ratio of Magnitude of average velocity and Average speed?​

Answer 1

$\mathfrak{\underline{\underline{\red{Question: }}}}$

A car travels for 4 hrs.Fir first 3 hours its goes away from the city A to city B its velocity is v1 and v2 for equal interval of time .In last 1 hr.it returns back with with velocity v3 and stops at some place between city A and city B . Find the ratio of Magnitude of average velocity and Average speed?

$\mathfrak{\underline{\underline{\red{Solution.•♫•♬•}}}}$

$\sf\pink{Let ~the ~total ~distance~ travelled ~be ~'x'.}$

$\sf\pink{Let ~the ~total ~time ~taken ~be~ T.}$

$\sf\pink{Average~ speed =\frac{ Total ~distance}{Total ~time} =\frac{ x}{T}}$

$\mathfrak{\underline{\underline{\red{First~half: }}}}$

${:⇒}$$\tt\purple{v = 10 km/h}$

${:⇒}$$\tt\purple{s = \frac{1}{3} x}$

${:⇒}$$\tt\purple{t= \frac{x}{\cancel{ \frac{3}{10}}}= \frac{x}{30}}$

$\mathfrak{\underline{\underline{\red{Second~half: }}}}$

${:⇒}$$\tt\green{v = 20 km/h}$

${:⇒}$$\tt\green{s =\frac{1 }{3} x}$

${:⇒}$$\tt\green{t= \frac{x}{\cancel{\frac{3}{20}}} = \frac{x}{60}}$

$\mathfrak{\underline{\underline{\red{Third~half: }}}}$

${:⇒}$$\tt\orange{v = 60 km/h}$

${:⇒}$$\tt\orange{s = \frac{1}{3}x}$

${:⇒}$$\tt\orange{t =\frac{ x}{\cancel{\frac{3}{60}}}=\frac{ x}{180}}$

$\mathfrak{\underline{\underline{\red{Now: }}}}$,

$\tt\pink{:⇒Time~ for~ entire ~journey, T~ =\frac{ x}{30 }+\frac{ x}{60 }+\frac{ x}{180}}$

$\mathfrak{\underline{\underline{\red{Now: }}}}$,

$\sf\purple{Average ~speed ~of~ the~ entire ~journey,~ Vav = \frac{Total~ distance}{Total time}}$

$\tt\purple{=\frac{ x}{\frac{x}{18}}}$

$\tt\purple{= 18 km/h}$

$\longrightarrow$The ratio of Magnitude of average velocity and Average speed is 18kmph.

Answer 2

$\huge\tt\colorbox{pink}{Answer}$

Let the total distance travelled be x

$\sf\pink{Let ~the ~total ~time ~taken ~be~ T.}$

$\sf\pink{Average~ speed =\frac{ Total ~distance}{Total ~time} =\frac{ x}{T}}$

$\mathfrak{\underline{\underline{\red{First~half: }}}}$

${:⇒}\tt\purple{v = 10 km/h}$

${:⇒} \tt\purple{s = \frac{1}{3} x}$

${:⇒} \tt\purple{t= \frac{x}{\cancel{ \frac{3}{10}}}= \frac{x}{30}}$

$\mathfrak{\underline{\underline{\red{Second~half: }}}}$

${:⇒} \tt\green{v = 20 km/h}$

${:⇒} \tt\green{s =\frac{1 }{3} x}$

${:⇒} \tt\green{t= \frac{x}{\cancel{\frac{3}{20}}} = \frac{x}{60}}$

$\mathfrak{\underline{\underline{\red{Third~half: }}}}$

${:⇒} \tt\orange{v = 60 km/h}$

${:⇒}\tt\orange{s = \frac{1}{3}x}$

${:⇒} \tt\orange{t =\frac{ x}{\cancel{\frac{3}{60}}}=\frac{ x}{180}}$

$\mathfrak{\underline{\underline{\red{Now: }}}}$

$\tt\pink{:⇒Time~ for~ entire ~journey, T~ =\frac{ x}{30 }+\frac{ x}{60 }+\frac{ x}{180}}$

$\sf\purple{Average ~speed ~of~ the~ entire ~journey,~ Vav = \frac{Total~ distance}{Total time}}$

$\tt\purple{=\frac{ x}{\frac{x}{18}}}$

$\tt\purple{= 18 km/h}$