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A passenger is standing d meters away fr...

A passenger is standing d meters away from a bus. The bus beings to move with constant acceleration a. To catch the bus, the passenger runs at a constant speed v towards the bus, What must be the minimum speed of the passenger so that he may catch the bus?

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Let the passenger catch the bus after time t, the distance travelled by the bus
`S_1` = 0 + `(1)/(2)at^(@)` (1)
And the distance travelled by the passenger
`S_2 = ut`
(2) Now passenger will catch the bus if
d.`S_1=s_2`   ...(3)
Substituting the values of `_1`, and `s_2` from equation (1) and (2) in (3), we get
`d+(1)/(2)at^(2)=ut`
i.e `(1)/(2)at^(2)-ut+d=0`So the passenger will catch the bus ift is real, f.e
So the minimum speed of passenger for catching the bus is `sqrt(2ad)`
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