A particle moves in a straight line a to b for the first one forth dis...
Given Data:
- Initial speed, v0
- Speed for the next half distance, 3v0
- Speed for the last one-fourth distance, 3v0
Calculating Average Speed:
To calculate the average speed, we need to find the total distance traveled and the total time taken.
Step 1: Finding Total Distance Traveled
Let the total distance be D.
- Distance covered in the first one-fourth = D/4
- Distance covered in the next half = D/2
- Distance covered in the last one-fourth = D/4
Therefore, total distance, D = D/4 + D/2 + D/4 = D
Step 2: Finding Total Time Taken
Let t1, t2, and t3 be the time taken to cover the first one-fourth, next half, and last one-fourth distance respectively.
- t1 = (D/4) / v0 = D / 4v0
- t2 = (D/2) / 3v0 = D / 6v0
- t3 = (D/4) / 3v0 = D / 12v0
Total time taken, T = t1 + t2 + t3 = D / 4v0 + D / 6v0 + D / 12v0 = D(1/4v0 + 1/6v0 + 1/12v0) = 7D / 12v0
Step 3: Calculating Average Speed
Average Speed = Total Distance / Total Time
Average Speed = D / (7D / 12v0) = 12v0 / 7
Therefore, the average speed of the particle moving from a to b is 12v0 / 7.