Mathematical and Physical Journal
for High Schools
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Problem P. 4606. (February 2014)

P. 4606. The motion of a pointlike mass can be split to two parts. In the first part its average speed is v1, and in the second its average speed is v2. For the whole motion the average speed is the geometric mean of the speeds v1 and v2, which is: \overline{v}=\sqrt{ v_1 v_2}. Determine the ratio of the covered distances in the two parts of the motion.

(4 pont)

Deadline expired on March 10, 2014.

Sorry, the solution is available only in Hungarian. Google translation

Megoldásvázlat. \(\displaystyle \frac{s_1}{s_2}=\sqrt{\frac{v_1}{v_2}}.\)

(Emellett még a nyilvánvaló megoldás: \(\displaystyle v_1=v_2\) esetén az utak aránya tetszőleges lehet.)


107 students sent a solution.
4 points:Balogh Menyhért, Berta Dénes, Fehér Zsombor, Horváth András Levente, Jakus Balázs István, Kacz Dániel, Radnai Bálint, Schefler Barna, Széles Katalin.
3 points:71 students.
2 points:10 students.
1 point:6 students.
0 point:9 students.
Unfair, not evaluated:2 solutions.

Problems in Physics of KöMaL, February 2014