87 km/h = 87/3.6 = 24.2 m/s
114 m/h/3.6 = 31.7 so 0 to 31.7 m/s in 12 s = 2.64 m/s^2
now
in time t
your speed u = 2.64 t
your distance = 1.32 t^2
how long do you take to get to 87 km/h = 24.2 m/s?
2.64 t = 24.2
t = 9.17 seconds to get to speed
you went
1.32 (9.17)^2 = 111 meters (about a football field)
how far did he go in that 9.17 s?
24.2 * 9.17 = 222 meters
so he is 22 meters behind you when you are both at the same speed
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 87 km/h. You have no choice but to join traffic and accelerate from rest as fast as your 15-year old Volkswagen allows (0-114 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?
3 answers
My last line is wrong
he is at 222 - 200 = 22 meters from the intersection
you are at 111 meters from the intersection
he is at 222 - 200 = 22 meters from the intersection
you are at 111 meters from the intersection
So why is it Distance = 1.32t^2 ???