Question

One goods train running at 54km/hr reaches station B from station A and comes back from B to A with a speed 45km/hr find average speed and velocity.

Answer 1

Answer:

The average speed = 540/11 km/h

The average velocity = 0 km/h

Explanation:

Given :

One goods train running at 54 km/hr reaches station B from station A and comes back from B to A with a speed 45 km/hr

To find :

the average speed and velocity

Solution :

Let the distance between station A and station B be 'x km'  

Station A to station B :  

speed = 54 km/h  

distance = x km  

time taken = ?

Speed = distance/time taken  

54 km/h = x km/ time taken  

time taken = x/54 hr

Station B to station A :  

speed = 45 km/h  

distance = x km  

time taken = ?

Speed = distance/time taken  

45 km/h = x km/time taken  

time taken = x/45 hr

Average speed :  

Total distance covered = x + x = 2x km  

total time taken = x/54 + x/45

 

Average speed = total distance covered/total time taken

 $\longrightarrow \sf \dfrac{2x}{\dfrac{x}{54} +\dfrac{x}{45}} \\\\\\ \longrightarrow \sf \dfrac{2}{\dfrac{1}{9}\bigg(\dfrac{1}{6}+\dfrac{1}{5} \bigg)} \\\\\\ \longrightarrow \sf \dfrac{2 \times 9}{\dfrac{5+6}{30}} \\\\\\ \longrightarrow \sf \dfrac{18}{\dfrac{11}{30}} \\\\\\ \longrightarrow \sf \dfrac{18 \times 30}{11} \\\\ \longrightarrow \sf \dfrac{540}{11} \ km/h$

Therefore, the average speed is 540/11 km/h

Average velocity :

As the train reached its starting point i.e., station A ; displacement is 0.

Average velocity = total displacement/total time taken

Average velocity = 0 km/h