Abus started from rest with a uniform acceleration of 2m/s. a mate who is 9m behind the bus runs after it immediately with a uniform speed of 6m/s. calculate the time taken for the mate to draw level with the rear of the bus.

The bus's position at time is

If we take the bus's rear's starting position to be the origin, then the position of the mate (?) is given by

The mate draws level with the rear of the bus when :

Drop the units to make things simpler:

So it would take 3 seconds for the mate to catch up to the bus.