A particle traversed half of the distance with a velocity of V_(0). The remaining parts of the distance was covered with velocity V_(1), for half of the time and with V_(2) for other half of the time. Find the mean velocity of the particle averaged and the whole time of motion

A particle traversed half of the distance with a velocity of V_(0). Th

1.	A particle traversed half of the distance with a velocity of V_(0). The remaining parts of the distance was covered with velocity V_(1), for half of the time and with V_(2) for other half of the time. Find the mean velocity of the particle averaged and the whole time of motion
Answer» SOLUTION : Average VELOCITY for the second HALF distance = `(v_(1)(t)/(2)+v_(2)(t)/(2))/((t)/(2)+(t)/(2))=(v_(1)+v_(2))/(2)` Average velocity for the first half distance = `V_(0)` (`because` it is constant) Average velocity for total path `=(2v_(0)((v_(1)+v_(2))/(2)))/(v_(0)+(v_(1)+v_(2))/(2))=(2v_(0)(v_(1)+v_(2)))/(v_(1)+v_(2)+2v_(0))`