Question

16.
A car travels with speed V1 for the first half of the journey time, during the second half of
the journey time it travelled with a speed of V2 for half of the distance and with a speed
of V3 for remaining journey distance. Find the average speed.​

Answer 1

REFER THE ABOVE PICTURE HOPE IT HELPS YOU

Answer 2

The average speed of the car is (2V1(V2+V3)/2V1+V2+V3).

Given:-

Speed for first half journey = V1

Speed for first half of rest journey = V2

Speed of remaining half of rest journey = V3

To Find:-

The average speed of the car.

Solution:-

We can simply calculate the average speed of the car by using these simple steps.

As

Speed for first half journey = V1

Speed for first half of rest journey = V2

Speed of remaining half of rest journey = V3

Now, let the total distance traveled by the car be D

According to the formula,

$speed = \frac{distance}{time}$

$time = \frac{distance}{speed}$

So, for first half journey

$t1 = \frac{ \frac{d}{2} }{v1}$

$t1 = \frac{d}{2 \times v1}$

for second half,

$t2 = \frac{d}{v2 + v3}$

Now, total time t =

$t = t1 + t2$

$t = (\frac{d}{2 \times v1} ) + (\frac{d}{v2 + v3} )$

$t = d( \frac{1}{2v1} + \frac{1}{v2 + v3} )$

$t = d(\frac{(v2 + v3 + 2v1)}{2v1(v2 + v3)} )$

Now,

$v(avg) = \frac{total \: distance}{total \: time}$

$v(avg) = \frac{d}{d(\frac{(v2 + v3 + 2v1)}{2v1(v2 + v3)} )}$

$v(avg) = \frac{1}{d(\frac{(v2 + v3 + 2v1)}{2v1(v2+ v3)} )}$

$v(avg) = \frac{2v1(v2 + v3)}{2v1 + v2 + v3}$

Hence, The average speed of the car is (2V1(V2+V3)/2V1+V2+V3).

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