A particle traversed on third of the distance with a velocity `v_(0)`, the remaining part of the distance was covered with velocity `v_(1)` for half the time and with a velocity `v_(2)` for the remaining half of time. Assuming motion to be rectilinear, find the the mean velocity of the particle averaged over the whole time of motion.

Explanation

For `AB,(S)/(3)=v_(0)t_(1)impliest_(1)=(S)/(3v_(0))` …(1)
for `CB,(2S)/(3)=CD+DB`
`implies(2S)/(3)=v_(1)((t_(2))/(2))+v_(2)((t_(2))/(2))impliest_(2)=(4S)/(3(v_(1)+v_(2))`
Since, average valocity is defined as
`v_("avg")=("Total displacement")/("total time")=((S)/(3)+(2S)/(3))/(t_(1)+(t_(2))/(2)+(t_(2))/(2))=(S)/(t_(1)+t_(2))`
`impliesV_("avg")=(3v_(0)(v_(1)+v_(2)))/(4v_(0)+v_(1)+v_(2))`