A block moves in a straight line with velocity v for time t_o.Then, its velocity becomes 2v for next t_o time.Finally,its velocity becomes 3v for time T. If avge.velocity during complete journey was 2.5v, then find T in terms of t_o.

Dear Chilukuri Kartik

distance travels in time t₀ with velocity v=vt₀

distance travels in time next t₀ with velocity 2v=2vt₀

distance travels in time _T with velocity 3v=3vT

total distance =vt_{0 +}2vt_{0 +}3vT

total time =t_{0 +}t_{0 +}T

so avg velocity ={vt_{0 +}2vt_{0 +}3vT}/{t_{0 +}t_{0 +}T}

                 2.5v     ={3vt_{0 +}3vT}/2t_{0 +}T}

or     2.5     =3{t_{0 +}T}/2t_{0 +}T}

simplify

T=4t₀

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