If a body travels half the distance with velocity v and next half with velocity v2, then which one of the following be the average velocity of the

The average velocity of a body is defined as the total distance covered divided by the total time taken. When a body travels two equal distance segments (half the distance each) with different velocities v1 and v2, the time taken for the first half is t1 = (d/2)/v1 and for the second half is t2 = (d/2)/v2. The total time is the sum of these intervals: t_total = (d/2v1) + (d/2v2) = d(v1 + v2) / (2v1v2). Substituting this into the average velocity formula (v_avg = d / t_total) yields v_avg = 2v1v2 / (v1 + v2). This result is the harmonic mean of the two velocities. The arithmetic mean (v1 + v2)/2 is only applicable if the time intervals, rather than the distances, were equal. Therefore, the correct expression for average velocity in this scenario is 2v1v2 / (v1 + v2).