Question: A point traversed half the distance with a velocity . The remaining part of the distance was covered with velocity for half the time, and with velocity for the other half of the time. Find the mean velocity of the point averaged over the whole time of motion.
Answer: Let the total distance be . Then, the first half was traveled in time .
After this, the remaining distance is .
Let this distance be covered in total of time of .
For , the point traversed at speed so the distance covered in this period is .
The remaining distance was covered at velocity and the distance covered at this speed is .
We have,
Thus, total time of travel is:
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