# A particle cover each 1/3 of the total distance with speed v1,v2 and v3 reapectively. Find athe average speed of the particle?

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Total distance S

Time to cover the first 1/3 of S = t1 = (S/3) / v1 = S/(3 v1)

Time to cover the second 1/3 of S = t2 = (S/3)/v2 = S/(3 v2)

Time to cover the last 1/3 of S = t3 = (S/3 ) / v3 = S/ (3v3)

Total time = t = S/3 [ 1/v1 + 1/v2 + 1/v3 ]

Let v = average speed

v = S / t So 1/v = t / S

*1/ v = 1/3 [ 1/v1 + 1/v2 + 1/v3 ] *

Time to cover the first 1/3 of S = t1 = (S/3) / v1 = S/(3 v1)

Time to cover the second 1/3 of S = t2 = (S/3)/v2 = S/(3 v2)

Time to cover the last 1/3 of S = t3 = (S/3 ) / v3 = S/ (3v3)

Total time = t = S/3 [ 1/v1 + 1/v2 + 1/v3 ]

Let v = average speed

v = S / t So 1/v = t / S