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A passenger is standing d metres away fr...

A passenger is standing `d` metres away from a bus. The bus begins to move eith constat acceleration `a. To catch the bus the passenger runs at a constant speed (v) towards the bus, at what minimum speed he must have ,so that he may catch the bus.

Text Solution

Verified by Experts

`S_("passenger") = d + S_("bus"), vt = d + (1)/(2)at^(2)`
`at^(2) - 2vt + 2d = 0 rArr t = (v pm sqrt(v^(2) -2ad))/(a)`
For minimum velocity
`v^(2) = 2ad = 0 rArr v = sqrt(2ad)`
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