T1a
Oberbefehlshaber der Somalier Genetik Gruppe
You run 2 laps of a track. V1 is the speed in the first lap, and V2 is the speed of the second lap. How fast does V2 need to be such that Vavg = 2V1 ?
When I first saw the problem I thought it's pretty simple.
If (V1 + V2)/2 = Vavg and Vavg= 2V1, it then follows that (V1 + V2)/2 = 2V1 and therefore V2 = 3V1.
But since V=D/T, the time must decrease in order to increase our speed. If you run the first lap in 10s, and the second lap in 10s, your average speed of lap 1 & 2 are the same. If you run lap 1 in 10s and lap 2 in 5s, the average speed will be Vavg= 2D/15, 15 is the total time, whereas the first lap the V1 = D/10 and the second lap V2 = D/5. The closest you could get is Vavg = 2D/10, where lap 2 is run in 0 seconds, and the speed is infinity. In this case, So this is in fact impossible since you would need to add negative time to increase the average speed to something above 1*V1.. can someone confirm??
When I first saw the problem I thought it's pretty simple.
If (V1 + V2)/2 = Vavg and Vavg= 2V1, it then follows that (V1 + V2)/2 = 2V1 and therefore V2 = 3V1.
But since V=D/T, the time must decrease in order to increase our speed. If you run the first lap in 10s, and the second lap in 10s, your average speed of lap 1 & 2 are the same. If you run lap 1 in 10s and lap 2 in 5s, the average speed will be Vavg= 2D/15, 15 is the total time, whereas the first lap the V1 = D/10 and the second lap V2 = D/5. The closest you could get is Vavg = 2D/10, where lap 2 is run in 0 seconds, and the speed is infinity. In this case, So this is in fact impossible since you would need to add negative time to increase the average speed to something above 1*V1.. can someone confirm??
