# Answer to Question #33368 in Mechanics | Relativity for shobhit

Question #33368

A body covers the half part of journey with the speed of S0 (S knot) for the remaining half part ot time it moves with the speed of S1 and remaing of the part with S2 .calculate the average speed.

Expert's answer

Average speed is total path (L) divided by total time of journey (t).

s_average=(L0+L1+L2)/(t0+t1+t2) (1)

From condition of the problem we have the following:

L0=L1+L2 (2)

t1=t2=t' (3)

from (2):

t0 * s0=t' * (s1+s2) (4)

Considering the (2)-(4) and definition of speed :

s_average=2L0/(t0+2t')=2t0*s0/(t0+2t')=2s0/(1+2t'/t0)=2s0/(1+2s0/(s1+s2))

Thus, the final answer

s_average=2s0(s1+s2)/(2s0+s1+s2)

s_average=(L0+L1+L2)/(t0+t1+t2) (1)

From condition of the problem we have the following:

L0=L1+L2 (2)

t1=t2=t' (3)

from (2):

t0 * s0=t' * (s1+s2) (4)

Considering the (2)-(4) and definition of speed :

s_average=2L0/(t0+2t')=2t0*s0/(t0+2t')=2s0/(1+2t'/t0)=2s0/(1+2s0/(s1+s2))

Thus, the final answer

s_average=2s0(s1+s2)/(2s0+s1+s2)

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