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A man traversed half the distance with a...

A man traversed half the distance with a velocity `v_(0)`. The remaining part of the distance was covered with velocity `v_(1)`. For half the time and with velocity `v_(2)` for the other half of the time . Find the average speed of the man over the whole time of motion.
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Text Solution

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Average velocity for the second half distance = `(v_1 t/2 + v_2 t/2)/(t_2+t_2)=(v_1+v_2)/2`
Average velocity for the first half distance = `v_0` ( `because` it is constant)
Average velocity for total path
`=(2v_0(v_1+v_2)/2)/(v_0+(v_1+v_2)/2)=(2v_0(v_1+v_2))/(v_1+v_2+2v_0)`
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