A person travels along a straight rod for half the distance with velocity $v_{1}$ and the remaining half distance with velocity $v_{2}$ , the average velocity is given by

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Solution

Total distance= $v_{1} t_{1} + v_{2} t_{2}$
Let total distance= $d$
$\frac{d}{2} = v_{1} t_{1}, t_{1} = \frac{d}{2 v_{1}}, t_{2} = \frac{d}{2 v_{2}}$
$v_{A y} = \frac{d}{t_{1} + t_{2}} = \frac{d}{\frac{d}{2} (\frac{1}{v_{1}} + \frac{1}{v_{2}})} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$

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A person travels along a straight rod for half the distance with velocity v1 and the remaining half distance with velocity v2, the average velocity is given by

Total distance=v1t1+v2t2Let total distance=dd2=v1t1,t1=d2v1,t2=d2v2vAy=dt1+t2=dd2(1v1+1v2)=2v1v2v1+v2

A person travels along a straight rod for half the distance with velocity $v_{1}$ and the remaining half distance with velocity $v_{2}$ , the average velocity is given by

Total distance= $v_{1} t_{1} + v_{2} t_{2}$
Let total distance= $d$
$\frac{d}{2} = v_{1} t_{1}, t_{1} = \frac{d}{2 v_{1}}, t_{2} = \frac{d}{2 v_{2}}$
$v_{A y} = \frac{d}{t_{1} + t_{2}} = \frac{d}{\frac{d}{2} (\frac{1}{v_{1}} + \frac{1}{v_{2}})} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$