First slide

Rectilinear Motion

Question

A car is travelling on a straight line moves with a uniform velocity V₁ for a distance 20m and with a uniform velocity V₂ for the next equal distance. Then the average velocity ‘V’ is given by…

Easy

A

$V = \sqrt{V_{1} V_{2}}$
B

$V = \frac{V_{1} + V_{2}}{2}$
C

$\frac{1}{V} = \frac{1}{V_{1}} + \frac{1}{V_{2}}$
D

$\frac{2}{V} = \frac{1}{V_{1}} + \frac{1}{V_{2}}$

Solution

$Time taken to travel a distance of 20 m is t_{1} = \frac{20}{V_{1}}$
$Time taken to travel next same distance of 20 is t_{2} = \frac{20}{V_{2}}$
$\begin{array}{l} : Averave velocity V = \frac{Total displacement}{Total time} \\ = \frac{20 + 20}{(\frac{20}{V_{1}}) + (\frac{20}{V_{2}})} \\ V = \frac{2}{(\frac{1}{V_{1}}) + (\frac{1}{V_{2}})} \end{array}$
$∴ \frac{2}{V} = \frac{1}{V_{1}} + \frac{1}{V_{2}}$

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