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Finding Average Velocity

A block moves...

Question

A block moves in a straight line with velocity v for time $t_{0} .$ Then, its velocity becomes 2v for next $t_{0}$ time. Finally its velocity becomes 3v for T. If average velocity during the complete journey was 2.5 v, then find T in terms of $t_{0} .$

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Solution

$v_{a v} = \frac{v t_{0} + 2 v t_{0} + 3 v T}{2 t_{0} + T} = 2.5 v \Rightarrow 2 t_{0} + 3 T = {5 t}_{0} + 2.5 T \Rightarrow T = 6 t_{0}$

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