A person travels along a straight road for the first half time with a velocity ${v_1}$ and the next half time with a velocity ${v_2}$ . The mean velocity $V$ of the man is
A person travels along a straight road for the first half time with a velocity ${v_1}$ and the next half time with a velocity ${v_2}$ . The mean velocity $V$ of the man is
$\frac{2}{V} = \frac{1}{{{v_1}}} + \frac{1}{{{v_2}}}$
$V = \frac{{{v_1} + {v_2}}}{2}$
$V = \sqrt {{v_1}{v_2}} $
$V = \sqrt {\frac{{{v_1}}}{{{v_2}}}} $
A person travels along a straight road for the first half time with a velocity ${v_1}$ and the next half time with a velocity ${v_2}$ . The mean velocity $V$ of the man is
For the first half time $= t$, velocity $= v _1$, distance $= s _1= v _1 t$
For the second half time $= t$, velocity $= v _2$, distance $= s _2= v _2 t$
Mean velocity $=\frac{ s _1+ s _2}{ t + t }=\frac{ v _1 t + v _2 t }{2 t }=\frac{ v _1+ v _2}{2}$