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Relative Velocity

A bus moving ...

Question

A bus moving with a speed of $10 m / s$ on a straight road. A scooterist wishes to overtake the bus in $100 s$ . If the bus is at a distance of $1 k m$ from the scooterist, with what speed should the scooterist chase the bus?

50 m / s

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40 m / s

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30 m / s

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20 m / s

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Solution

The correct option is A $20 m / s$
Let the velocity of the scooterist $= ν$
Relative velocity of scooterist with respect to bus $= (ν - 10)$
$\Rightarrow S = (ν - 10) \times 100 \Rightarrow 1000 = (ν - 10) \times 100$
$∴ ν = 10 + 10 = 20 m / s$

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