An amusement park ride features a vertical cylinder 8 m in radius with a horizontal floor. Riders stand on the floor with their backs against the inner surface of the cylinder. The cylinder spins, completing one revolution every 4s. Once spinning, the axis of the cylinder rotates so it tilts up to 45 degrees. Even as the cylinder tilts
sideways, the riders don't fall off

1. What direction is the force exerted by the cylinder on the riders?

2. What is the angular velocity of the riders?

3. What is the linear velocity of the riders?

4. What centripetal acceleration do the riders experience?

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.

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