A body moving along a straight line traversed one third of the total distance with a velocity `4 m//sec` in the first stretch. In the second strech the remaining distance is covered with a velocity `2 m//sec` for some time `t_(0)` and with `4 m//s` for the remaining time. if the average velocity is `3 m//sec` find the time for which body moves with velocity `4 m//sec` in second strecth:

Options

A. `(3)/(2)t_(0)`
B. `t_(0)`
C. `2t_(0)`
D. `(t_(0))/(2)`

Answer

D

Explanation

Sol: `t_(1)=(s//3)/(4)=(s)/(12)`
`(2s)/(3)=2(t_(0))+4(kt_(0))=t_(0)(2+4k)ort_(0)=(2s)/(3(2+4k))`
`"Average velocity"=(s)/(t_(1)+t_(0)+t_(0)k)`
`=(s)/((s)/(12)+(2s(1+k))/(3(2+4k)))=(6(2+4k))/((5+6k))`
`V_(av)(5+6k)=12+24k` gives `k=(1)/(2)`
Required time `=kt_(0)=(t_(0))/(2)`