Question

A train Start from one station reaches second station in 3 hr which is at 48 km away from first
station. And then returns back to the first station and takes 5 hr. Find the Average speed and average
velocity of the train​

Answer 1

Explanation:

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

• Time taken by train from one station (Station 1) to second station (Station 2) = 3 hrs

• Time taken by train from second station (Station 2) to one station (Station 1) = 5 hrs

• Distance between station one and second station = 48 km

We are asked to calculate average speed and average velocity of the train.

★ Calculating average speed of the train :

Average speed refers to the total distance covered divided by total time.

$\\ \longrightarrow \quad \pmb{\boxed{\sf {Speed_{(avg)} = \dfrac{Total \; distance}{Total \; time }}}}$

$\\ \longrightarrow \sf{\quad Speed_{(avg)} = \dfrac{Distance_{(Station \; 1 \; to \; 2)} + Distance_{(Station \; 2 \; to \; 1) }}{Time_{(Station \; 1 \; to \; 2)} +Time_{(Station \; 2 \; to \; 1)}} }$

$\\ \longrightarrow \sf{\quad {Speed_{(avg)} = \dfrac{(48 + 48) \; km }{(3 + 5) \; hrs} }}$

$\\ \longrightarrow \sf{\quad {Speed_{(avg)} =\cancel{ \dfrac{ 96 \; km }{ 8\; hrs}} }}$

$\\ \longrightarrow \bf{\quad {\underline{ Speed_{(avg)} = 12 \; km/h}}}$

Therefore, average speed of the train is 12 km/h.

★ Calculating average velocity :

Average velocity refers to the total displacement divided by total time.

$\\ \longrightarrow \quad \pmb{\boxed{\sf {Velocity_{(avg)} = \dfrac{Total \; displacement}{Total \; time }}}}$

The train came back to its initial position after covering certain distance. Whenever tha body comes back to its initial position after covering certain distance, then its displacement is 0.

$\\ \longrightarrow \sf{\quad {Velocity_{(avg)} = \dfrac{0\; km }{ (3 + 5) \; hrs} }}$

$\\ \longrightarrow \sf{\quad {Velocity_{(avg)} =\cancel{ \dfrac{ 0 \; km }{ 8\; hrs}} }}$

$\\ \longrightarrow \bf{\quad {\underline{ Velocity_{(avg)} = 0 \; km/h}}}$

Therefore, average velocity of the train is 0 km/h.