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
To determine how close the following car comes up behind you, we can calculate the distance it covers while your Volkswagen accelerates from 0 to 110 km/h.
First, let's convert the speeds to meters per second (m/s) for a consistent unit:
90 km/h = (90 * 1000) / (60 * 60) = 25 m/s
110 km/h = (110 * 1000) / (60 * 60) = 30.5 m/s
Next, we need to calculate the time it takes for your Volkswagen to reach 110 km/h:
12 seconds = 12 seconds
Now, let's calculate the distance covered by the car traveling at a constant speed of 25 m/s during that time:
Distance = Speed * Time
Distance = 25 m/s * 12 seconds = 300 meters
Therefore, the following car would come up behind you at a distance of 300 meters.
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