When travelling in a city, it can often be faster to use a bicycle than to take a bus.
One reason for this is that bikes are able to accelerate faster than buses can.
Now, let's say that a bike and a bus both stopped at a red light,
take off at the exact same time when the light turns green.
The bike can accelerate at 1.2 m/s² but only to a top speed of 12 m/s.
The bus on the other hand can accelerate at 0.8 m/s² to a top speed of 20 m/s.
Now, since the bike has a higher initial acceleration,
it will be in front of the bus for some time.
I want to know how much time elapses before the bus catches up with the biker.