You are stopped at the end of the merge lane at the entrance to a motorway because traffic is dense with cars at a distance of 200m from each other with no larger gaps in sight. They are all travelling at a steady 90 km/h. You have no choice but to join traffic and accelerate from rest as fast as your 15-year old Volkswagen allows (0-110 km/h in 12s). You start accelerating directly after a car passes you. Assuming that the following driver does not slow down to let you in, how close does he come up behind you? Answer in metres

1 answer

the time to reach traveling speed is ... (90 / 110) * 12 ... seconds

your average speed during this time is ... (90 - 0) / 2 ... kph

how far do you travel?

how far does the closing car travel?
... its going twice as fast as you

the closest approach is the difference in travel distances
... with the 200 m head start accounted for