$n$ cars are travelling down a narrow one-way street. We know that:
- The distance $d$ between each two cars is the same.
- The safe breaking distance $b$ is the minimum distance between two cars that is needed for the second car to stop on time if the car in front suddenly breaks.
- $d < b$
Prove by induction or refute: if the first car suddenly stops moving, all cars will stop moving. Before you do the induction state the property $P$ you are using in the induction axiom.
What I came up so far:
Base case: $n=1$
if there is only one car traveling down a narrow one way street, than obviously only 1 car will stop moving -> therefore the assertion is true
Induction step: $n= k+1$
I am stuck here---- need a hint