Question

A bus starts from rest, moves with a uniform acceleration â€a’. Simultaneously a passenger at a distance x from the bus starts running to catch the bus. The minimum velocity of the passenger to catch the bus is

Answer 1

Now let the passenger catch the bus at time t, with a velocity v.

Now distance traveled in time t by the passenger= Distance traveled by the bus in time t + initial separation between them i.e. X .( Under this condition only the passenger can catch the bus.)

or v*t = 1/2*a*t^2 + X

Now we get a quadratic equation in t

or a*t^2 - 2v*t + X = 0

Now the logic is simple, the passenger will catch the bus after a certain time. So the passenger can catch the bus only when time is a real number. So the quadratic equation must give t as a real number.

For that the discriminant (D) of the equation must be greater than or equal to zero.

So 4*v^2=8*a*X

or v^2=2*a*X