Given, t1= T, t2 = 2T
s1 = v1 x t1 = v1(T) = Tv1
s2 = v2 x t2 = v2(2T) = 2Tv2
Total displacement = s1 + s2 = T(v1 + 2v2)
Total time = t1 + t2 = 3T
average velocity = T(v1 + 2v2)/3T = (v1 + 2v2)/3

Problem Statement: A particle moves in straight line with velocity v1 and v2 for time interval which are in ratio 1:2 find average velocity?

Solution:

Step 1: Understanding the problem
Let's first understand the given problem. We are given two velocities v1 and v2 and the time intervals for which the particle moves with these velocities are in ratio 1:2. We need to find the average velocity of the particle.

Step 2: Calculating total time
Let's assume that the particle moves with velocity v1 for time t1 and with velocity v2 for time t2. As per the given problem, t2 = 2t1. Therefore, the total time taken by the particle is:
t = t1 + t2 = t1 + 2t1 = 3t1

Step 3: Calculating distance traveled
Let's assume that the particle covers a distance d1 with velocity v1 and a distance d2 with velocity v2. Therefore, we have:
d1 = v1*t1 and d2 = v2*t2 = v2*2t1
The total distance covered by the particle is:
d = d1 + d2 = v1*t1 + v2*2t1 = (v1 + 2v2)*t1

Step 4: Calculating average velocity
The average velocity of the particle is given by the ratio of total distance and total time:
v_avg = d/t = (v1 + 2v2)*t1 / 3t1 = (v1 + 2v2)/3

Therefore, the average velocity of the particle is (v1 + 2v2)/3.

Conclusion: In this way, we can calculate the average velocity of a particle when it moves with two different velocities for different time intervals.