Question

a car travels half the distance by 20m/s and another half distance by 30m/s, the average speed of the car will be:
a)0m/s b)25m/s c)10m/s d)24m/s

Answer 1

The car travels half the distance by 20 m/s and the other half of the distance by 30 m/s .

Let the total distance be 2 x such that the half distance is x .

Let the total time taken be T .

Let the time taken for the first distance be t1 and the second distance be t2 .

So we can write that T = t1 + t2 because the total time taken is the sum of the time taken for the first half and the time taken for the second half .

Let the average speed be S .

Speed = distance / time

⇒ time = distance / speed

For the first distance

t1 = x / ( 20 )

⇒ t1 = x / 20

For the second distance

t2 = x / ( 30 )

⇒ t2 = x / 30

For the whole distance

T = 2 x / S

Adding t1 + t2 gives T

T = t1 + t2

⇒ T = x / 20 + x / 30

⇒ 2 x / S = x ( 1/20 + 1/30 )

⇒ 2 / S = ( 1/20 + 1/30 )

⇒ 2 / S = ( 3 + 2 ) / 60

⇒ 2 / S = 5 / 60

⇒ 2 / S = 1 / 12

⇒ S = 12 × 2

⇒ S = 24

OPTION D : The average speed will be 24 m/s .

Answer 2

$<b>ANSWER !$

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Let the total distance covered be s metre

Half distance = s/2 metre

Speed of car in first half = 20m/s

Let time taken be t

We know,

Speed = Distance/Time

=> 20 = s/2 × 1/t

=> s = 40t

=> t = s/40 sec --------------- ( 1 )

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Half diatance = s/2 metre

Speed of the car in second half = 30m/s

Let the time taken be t


=> 30 = s/2 × 1/t

=> s = 60t

=> t = s/60 sec ---------------- ( 2 )


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Total time taken to cover the distance =

Adding ( 1 ) and ( 2 ), we get

=> s/40 + s/60

=> ( 3s + 2s )/120

=> 5s/120 sec


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Average speed = Total Distance Travelled/Total Time Taken

Total diatance = s metre

Total time = 5s/120 sec


Average speed =

=> s × 120/5s

=> 120/5

=> 24 m/s ANS



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#BE BRAINLY