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Q.

A body moving along a straight line travels one third of the total distance with a velocity 4 m/s The remaining distance is covered with velocity 2 m/s for some time $t_{0}$ and with 4m/s for the remaining time. If the average velocity is 3 m/s, then the time for which the body moves with velocity 4 m/s in second stretch is

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a

$t_{0}$

b

$2 t_{0}$

c

$\frac{t_{0}}{2}$

d

$\frac{3}{2} t_{0}$

answer is D.

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Detailed Solution

$t_{1} = \frac{s / 3}{4} = \frac{s}{12} \frac{2 S}{3} = 2 t_{o} + 4 (K t_{0}) \Rightarrow t_{0} = \frac{2 s}{3 (2 + 4 k)} < \bar{v} > = \frac{s}{t_{1} + t_{0} + t_{0}} = 3 \frac{6 (2 + 4 k)}{5 + 6 k} = 3 k = \frac{1}{2} \Rightarrow r e q u i r e d t i m e = \frac{t_{0}}{2}$

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