1.

A train covers one half of the distance between two stations with an average speed V1 and remaining half with an average speed V2 . Let V denote the average speed of the train for the whole journey. Show that 1 V = 1 2 [ 1 V1 + 1 V2 ]​

Answer»

Answer:

EXPLANATION:

If The HALF distance (x) covered with the speed v  

1

​

 in t  

1

​

 time.

Using formula of speed, v  

1

​

=  

t  

1

​

 

x

​

 

so, t  

1

​

=  

v  

1

​

 

x

​

 

And another half distance (x), covered with speed v  

2

​

 in time t  

2

​

.

so, v  

2

​

=xt  

2

​

 

t  

2

​

=  

v  

2

​

 

x

​

 

Average VELOCITY=  

TOTAL time

Total distance

​

 

Total time=t  

1

​

+t  

2

​

=  

v  

1

​

 

x

​

+  

v  

2

​

 

x

​

 

=  

v  

1

​

v  

2

​

 

(v  

2

​

∗x+v  

1

​

∗x)

​

 

Total distance =x+x=2x

On putting the VALUES of total distance and total time in the formula of average speed, we get

Average speed=  

(  

v  

1

​

∗v  

2

​

 

v  

2

​

x+v  

1

​

x

​

)

2x

​

 

V=  

(v  

1

​

+v  

2

​

)

2v  

1

​

v  

2

​

 

​


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