​​Q. A POINT TRAVERSED (1/N)TH THE DISTANCE WITH A VELOCITY V0. THE REMAINING PART OF DISTANCE WAS COVERED WITH VELOCITY V1 FOR HALF THE TIME, AND WITH VELOCITY V2 FOR THE OTHER HALF OF THE TIME. FIND THE MEAN VELOCITY OF THE POINT AVERAGED OVER THE WHOLE TIME OF THE MOTION.

4N/(4V₀+N-1)

ITS ABSOLUTELY WRONG ANSWER. PLEASE TELL THE RIGHT ANSWER ALONG WITH PROPER EXPLANATION.

THE ANSWER IS:

 

NV0 (V1+V2)/[2(N-1) V0 +V1+V2]

explanation please althought the ans is correct

Yes,I am wrong. The 

Yes, I am wrong. The right answer is explained below:                                                                                          Let total distance = S, Time required(t1)Total time to cover the distance with velocity V0 = S/NV0. Remaining part of the distance = S – S/N =S(N-1)/N. If this distance is covered in time 2t,                                                              V1.t+V2.t =S(N-1)/N .  Therefore t = S(N-1)/N(V1+V2).                                                           So Vavg = Net displacement/Total time = S/(S/NV0 +2S(N-1)/N(V1+V2))                                                        = NV0(V1+V2)/ (V1+V2+2V0(N-1))