Catching the bus problem

A man is standing 40 m behind the bus. Bus starts with 1 m/s2 const. acceleration and also at same instant the man starts moving with constant speed 9 m/s. Find the time taken by the man to catch the bus?

 

First of all, imagine after time t, he will get the bus.

By that time the bus will move to a distance,

So, 

                                                 

By that time he should run the distance, 

From (1) and (2) , we have ,        

Solving this quadratic equation you will get, t =8 sec or 10 sec.