Puzzles/Physics puzzles/Train on Circle/Solution
The train would need to be infinitely fast.
The train is required to double its average velocity, so it was travel twice as far in the same amount of time. The first loop has already been travelled in a set time, and makes up half the distance, so the other half of the distance must to be completed in no time (so the train has travelled double the distance in the same amount of time). The train must travel infinitly fast to achieve this.
Since this is a "physics" puzzle....velocity is vector. A train going in a circle at ANY speed would have an average velocity of zero.
- The solution seems wrong to me.
Let t1 be the time taken for the first round and t2 for the second round. Let s1, s2 be the average speed and r the radius. Then
100 = 2*Pi*r/t1 => t1 = 2*Pi*r/100
200 = 4*Pi**r/(t1 + t2)
t2 = 1/100
s2 = 2*Pi*r/t2 => s2 = 200*pi*r
- Two additional comments
Yes, the average velocity (a vector) would be zero. The average speed (a scalar) would have to be infinite tho.
The calculations made in the Comment section above are wrong. If 100 = 2*Pi*r/t1, then 200 = 4*Pi*r/(t1 + t2) only if t2 is zero. Hence, t2 = 1/100 is not true.