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, What must so that he may catch the bus.

Explanation

Let the passenger catches the bus after time Distance travelled bu the in time (t),
` S_91) =0 + 1/2 at^(2) = 1/2` …(i)
Distance travelled by the passenger, (ii) ` S_(2) =v t + 0 v t`
The passenger will catch the bus if,
` d+ S_(1) = S_(2)`
or ` d + 1/2 at^(2) =v t or 1/2 at^(2) - v t + d =0`
or ` t= =([v+- sqrt(v^(2) -2 a d)}])/a`
The passenger will catch the bus it 9t) is real,
i.e. `v^(2) gt- 2 a d or v gt- sqrt2 ad`
Thus minimum speed passenger for catching the bus in ` sqrt 2 ad`.