Thank you sir for answering my question. But I have a doubt here ,please clear it.Why the final velocity of passanger is 0 wrt bus in case of minimum speed require for passanger to catch the bus.Is it 0 only for this situation or for all other situations??

When the passenger will reach the bus then the bus and the passenger should be moving in the same velocity so that he can enter into the bus I mean then with respect to the bus the man running outside will be appearing to be stationary here we are talking about the concept of relative motion so so we are observing the man running with respect to a man sitting inside the bus I that is I send initially it's enough that we are considering this first to be stationary and the man is running that means that last the man should end up being stationary so that a man sitting inside the bus will see this man running approaching and finally being stationary and getting inside the bus