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SHM expression

a body moving...

Question

a body moving along a straight line travels 3/5^th part of total distance with speed v1 and remaining part with speed v2. find average speed of body.

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Solution

Let S be the total distance to be travelled.
It travels (3/5)S with speed v₁. Time taken is t₁ = [(3/5)S/v₁] = 3S/5v₁
Next (2/5)S is travelled with speed v₂. Time taken is t₂ = [(2/5)S/v₂] = 2S/5v₂
So, average speed = total distance/total time = S/[3S/5v₁ + 2S/5v₂] = 5/[3/v₁ + 2/v₂] = 5v₁v₂/(3v₂ + 2v₁)

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