A body moves in a straight line with speed V1 and V2 for distance X1 and X2 . X1 and X2 are in the ratio 1 : 2 .Find the average speed.
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Given info : A body moves in a straight line with speed v₁ and v₂ for distance x₁ and x₂. x₁ and x₂ are in the ratio of 1 : 2.
To find : the average speed.
solution : we know, average speed = total distance/total time.
case 1 : time , t₁ = distance/speed = x₁/v₁
case 2 : time, t₂ = distance/speed = x₂/v₂
so, average speed = (x₁ + x₂)/(t₁ + t₂)
= (x₁ + x₂)/(x₁/v₁ + x₂/v₂)
a/c to question, x₁/x₂ = 1/2
= (x₁ + 2x₁)/(x₁/v₁ + 2x₁/v₂)
= 3/(1/v₁ + 2/v₂)
= 3v₁v₂/(v₂ + 2v₁)
Therefore the average speed of the body is 3v₁v₂/(v₂ + 2v₁)
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