Question

a body starts from reaches to at the rate of 40 km H and return at the rate of 60 km h find the average speed of velocity of whole journey​

Answer 1

Appropriate Question:

A body starts from A reaches to B at the rate of 40 km/h and return at the rate of 60 km/h. Find the average speed and average velocity of whole journey.

Answer:

Average speed = 48 km/h

Average velocity = 0 km/h

Explanation:

As per the provided information in the given question, we have :

• A body starts from A reaches to B at the rate of 40 km/h and return at the rate of 60 km/h.

We've been asked to calculate average speed and average velocity.

In order to calculate the average speed, we need to calculate the total distance travelled and total time taken first.

»⠀Let us assume the distance from A to B as x km. As the body starts from A reaches to B at the rate of 40 km/h and return at the rate of 60 km/h. So,

↠⠀⠀⠀Total distance = AB + BC

↠⠀⠀⠀Total distance = (x + x) km

↠⠀⠀⠀Total distance = 2x km

Now, we have to calculate total time. Total time taken will be the sum of time taken from A to B and from B to A.

• Distance from A to B = x km
• Speed from A to B = 40 km/h
• Distance from B to A = x km
• Speed from B to A = 60 km/h

As we know that,

⠀⠀⠀⠀⠀⠀⠀○ Time = Distance ÷ Speed

$\twoheadrightarrow \sf{\quad {Time_{(Total)} = Time_{(AB)} + Time_{(BA)} }}$

$\twoheadrightarrow \sf{\quad {Time_{(Total)} = \dfrac{Distance_{(AB)}}{Speed_{(AB)}} + \dfrac{Distance_{(BA)}}{Speed_{(BA)}} }}$

$\twoheadrightarrow \sf{\quad {Time_{(Total)} = \Bigg \{ \dfrac{x}{40} + \dfrac{x}{60} \Bigg \} \; h}}$

$\twoheadrightarrow \sf{\quad {Time_{(Total)} = \Bigg \{ \dfrac{3x+ 2x}{120} \Bigg \} \;h }}$

$\twoheadrightarrow \sf{\quad {Time_{(Total)} = \Bigg \{ \dfrac{5x}{120} \Bigg \} \; h}}$

$\twoheadrightarrow \bf{\quad {Time_{(Total)} = \dfrac{x}{24} \; h}}$

Now, we have to calculate the average speed.

$\bigstar \quad \underline{\boxed { \pmb{\frak{ Speed}}_{\pmb{\frak{(Avg) }} } = \dfrac{\pmb{\frak{ Distance}}_{\pmb{\frak{(Total) }} } }{\pmb{\frak{ Time}}_{\pmb{\frak{(Total) }} } } }}$

$\twoheadrightarrow \sf{\quad { Speed_{(Avg)} = \Bigg \{ 2x \div \dfrac{x}{24} \Bigg \} \; km \: h^{-1} }}$

$\twoheadrightarrow \sf{\quad { Speed_{(Avg)} = \Bigg \{ 2x \times \dfrac{24}{x} \Bigg \} \; km \: h^{-1} }}$

$\twoheadrightarrow \sf{\quad { Speed_{(Avg)} = \Bigg \{ 2 \times 24 \Bigg \} \; km \: h^{-1} }}$

$\twoheadrightarrow \quad\underline{\boxed { \bf Speed_{(Avg)} = 48 \; km \: h^{-1} }} \;\bigstar$

⠀⠀⠀__________________________⠀⠀⠀⠀⠀⠀

In order to calculate average velocity, we need to find total displacement and total time.

As the body comes back again to its initial position after covering certain distance. Thus, its displacement is 0. And so total displacement is also 0.

We've already calculated total time in the first part of the question.

$\bigstar \quad \underline{\boxed { \pmb{\frak{ Velocity}}_{\pmb{\frak{(Avg) }} } = \dfrac{\pmb{\frak{ Displacement}}_{\pmb{\frak{(Total) }} } }{\pmb{\frak{ Time}}_{\pmb{\frak{(Total) }} } } }}$

$\twoheadrightarrow \sf{\quad { Velocity_{(Avg)} = \Bigg \{ 0 \div \dfrac{x}{24} \Bigg \} \; km \: h^{-1} }}$

$\twoheadrightarrow \quad\underline{\boxed {\bf Velocity_{(Avg)} = 0 \; km \: h^{-1} }} \;\bigstar$

Therefore, average speed is 48 km/h and average velocity is 0 km/h.