1. A single cylinder horizontal engine runs at 120 r. p.m. The length of stroke is 400 mm. Themass of the revolving parts assumed concentrated at the crank pin is 100 kg and mass of thereciprocating parts is 150 kg. Determine the magnitude of the balancing mass required to beplaced opposite to the crank at a radius of 150mm which is equivalent to all the revolving and 2/3 * r * d of the reciprocating masses. If the crank turns 30° from the inner dead centre, find themagnitude of the unbalanced force due to the balancing mass. ​

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.