A particle moves half distance by 20 m/s and stay half distance moves by 30 m/s. Average speed of total journey should be?
To find the average speed of the total journey, we need to consider the distances traveled and the time taken for each segment of the journey.
Let's assume the total distance traveled is D.
According to the problem, the particle covers the first half of the distance at a speed of 20 m/s. This means it travels D/2 distance at a speed of 20 m/s.
Similarly, the particle covers the second half of the distance at a speed of 30 m/s. This means it also travels D/2 distance at a speed of 30 m/s.
Let's calculate the time taken for each segment:
Time taken for the first half: (D/2) / 20 = D/40 seconds
Time taken for the second half: (D/2) / 30 = D/60 seconds
The total time taken for the journey is the sum of the times taken for each segment:
Total time taken = (D/40) + (D/60)
To find the average speed, we divide the total distance by the total time:
Average Speed = Total distance / Total time
Substituting the values:
Average Speed = D / [(D/40) + (D/60)]
To simplify this equation, we take the least common multiple (LCM) of the denominators, which is 120:
Average Speed = D / [(3D + 2D) / 120]
Average Speed = D / (5D / 120)
Average Speed = D * (120 / 5D)
Average Speed = 24 m/s
Therefore, the average speed of the total journey is 24 m/s.