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Derivation of Velocity-Time Relation by Graphical Method

A person trav...

Question

A person travelling on a straight line moves with a uniform velocity v₁ for some time and with uniform velocity v₂ for the next equal time. The average velocity v is given by
(a) $v = \frac{v_{1} + v_{2}}{2}$
(b) $v = \sqrt{v_{1} v_{2}}$
(c) $\frac{2}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$
(d) $\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$

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Solution

(a) $v = \frac{v_{1} + v_{2}}{2}$

Velocity is uniform in both cases; that is, acceleration is zero.
We have:
$d_{1} = v_{1} t$ and $d_{2} = v_{2} t$
Total displacement, $d = d_{1} + d_{2}$
Total time, $t = t + t = 2 t$
$∴$ Average velocity, $v = \frac{d_{1} + d_{2}}{2 t} = \frac{v_{1} + v_{2}}{2}$

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Similar questions

v = \frac{v_{1} + v_{2}}{2}

v = \sqrt{v_{1} v_{2}}

\frac{2}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}

\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}

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