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These test problems were used by the author as weekly control works for the first year physics students at Novosibirsk State University in 2005. Solutions of the problems are also given. The problems were taken from or inspired by the sources that are listed at the end of the book. Some problems are fairly hard to solve and their main purpose is just to communicate some interesting facts to the students. The problems are arranged according to the program of the introductory mechanics course adopted at Novosibirsk State University. The following textbook (in Russian) Yu.I. Belchenko, E.A. Gilev, Z.K. Silagadze, Problems in mechanics of particles and bodies (http://shop.rcd.ru/details/1121), contains much more problems that have been used in seminars, students' homework and in the written examinations during many years.