A Passenger Is Standing ‘d’ m away From A Bus. The Bus Being 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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Question

diffcult

Correct option is

Let the passenger catch the bus after time t. From 2^nd equation of motion, the distance travelled by the bus,

and the distance travelled by the passenger

s₂ = ut + 0 …(2)

Now the passenger will catch the bus if

d + s₁ = s₂ …(3)

Substituting the values of s₁ and s₂ from Eqns. (1) and (2) in (3), we get

So the passenger will catch the bus if t is real, i.e.,

So the minimum speed of passenger for catching the bus is