a particle covers 1/2 distance between A and B with a velocity V0. during 1/2 of the time required to cover the remaining distance the particle moves with a velocity V1 and rest moves with a velocity V2. find the average velocity of the particle

avg velocity= total distance/total time

= (vo*t+ v2*t2+v1*t1)/(t+t2+t1)

To find the average velocity of the particle, we need to determine the total distance traveled and the total time taken.

Let's assume the total distance between A and B is represented by "d".

The particle covers 1/2 of the distance with a velocity V0. This means the distance covered with velocity V0 is (1/2)d.

The remaining distance to be covered is also (1/2)d.

Now, during 1/2 of the time required to cover the remaining distance, the particle moves with velocity V1, and for the rest of the time, it moves with velocity V2.

Let's assign the time required to cover the remaining distance as "t".

During the first (1/2)t time period, the particle moves with velocity V1. Therefore, the distance covered during this time is (V1 * (1/2)t).

During the remaining (1/2)t time period, the particle moves with velocity V2. Therefore, the distance covered during this time is (V2 * (1/2)t).

Hence, the total distance covered is ((V1 * (1/2)t) + (V2 * (1/2)t) + (1/2)d).

The total time taken is ((1/2)t + (1/2)t + t) = (2t).

The average velocity is calculated by dividing the total distance by the total time:
Average velocity = Total distance / Total time = ((V1 * (1/2)t) + (V2 * (1/2)t) + (1/2)d) / (2t)

Simplifying this expression gives the average velocity of the particle.