Question

a train travels with a speed of 60 km/h from station a to b and then comes back with a speed of 80 km/h from b to a.find:-(1) the average speed of the train (2) the average velocity of the train.​

Answer 1

Given that, a train travels with a speed of 60 km/hr from station A to B. Here, station A is the initial point from where the train starts and the point B is the final point where train reaches. (S1 = 60 km/hr)

Also given that, after reaching station B, it returns back to station A with a speed of 80 km/hr. (S2 = 80 km/hr)

We have to find the (1) the average speed of the train (2) the average velocity of the train.

Average speed is defined as the ratio of total distance covered by body or train with respect to total time taken.

1) Let us assume that the distance travelled by the train from station A to B is x and from station B to A is also x.

Total distance covered by train = (x + x) = 2x km

Time = Distance/Speed

From station A to B: (t1)

t1 = x/60 hr

From station B to A: (t2)

t2 = x/80 hr

Total time taken by train = t1 + t2 = x/60 + x/80 = 7x/240

Average speed = 2x/(7x/240) = (2x × 240)/7x = 68.6 km/hr

2) Average velocity is defined as the ratio of total displacement with respect to total time taken.

Now, as train starts from station A to station B and then returns back to station A. The starting point to train is station A and its ending point is also A. So, displacement of the train is 0.

Average velocity = 0/(7x/240) = 0 km/hr

Answer 2

$\bigstar$ Solution :

$\bigstar$ Given :

• A train travels with a speed of 60 km/h from station a to b and then comes back with a speed of 80 km/h from b to a

$\bigstar$ To Find :

1. The average speed of the train
2. The average velocity of the train.​

$\bigstar$ Explanation :

$\bigstar$ Average Speed :

$\star$ Average speed is defined as the ratio of total distance covered by body with respect to the total time taken

( 1 )

$\star$ Let us assume that distance traveled by the train from station A to B is x .

$\star$ So the distance B to A is also x .

• $Speed=\frac{Distance}{Time}$

$=>Time=\frac{Distance}{Speed}$

$\star$ From Station A to B. Let it be $t_1$

=> $t_1=\frac{x}{60}$

$\star$ From Station B to A. Let it be $t_2$

=> $t_2=\frac{x}{80}$

$\star$ Now , Total time = $t_1+t_2$

$=>t=\frac{x}{60} +\frac{x}{80}\\\\ =>t=\frac{140x}{4800} \\\\=>t=\frac{7x}{240}$

Now , Average speed = $\frac{TotalDistance}{Time}$

=> Average Speed = $\frac{x+x}{\frac{7x}{240} }$

=> Average Speed = 480x / 7x

=> Average Speed = 68.6 km/hr

                                                                                                 

$\bigstar$ Average Velocity :  

$\star$ Average velocity is defined as the ratio of total displacement with respect to total time taken.

( 2 )  

$\star$ Here The train travels with a speed of 60 km/h from station A to B and then comes back with a speed of 80 km/h from B to A.So the displacement is 0.

$\star$ So Average Velocity = Total Displacement / Time

$=>A_v =\frac{0}{t}\\\\ =>A_v=0$

                                                                                                   

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