Question

a particle transversed along a straight line for first half time with velocity V0 for the remaining part half of the distance is transversed with velocity V1 and other half distance with velocity V2 find the mean velocity of the particle for total journey .



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Answer 1

Let the total distance be D.

Let the point transversed half the distance by velocity V1.

Then the time required by it to do so = (D/2)/V1 = D/2V1

The remaining half was transversed by travelling at V2 for halftime and V3 velocity for another half time.

Let the time to cover the second half of the journey = t

Then V2t/2+V3t/2= D/2(Second Half of journey)

So t= D/(V2+V3)

The total time required for the journey is (D/2V1)+(D/(V2+V3))

The Average or mean Velocity = D/( (D/2V1) + (D/(V2+V3)) ) = 1/( (1/2V1) + (1/(V2+V3))) =2V1(V2+V3)/(2V1+V2+V3)-----(ans)