A 1030 kg roller coaster goes over hill and through a valley, then upside down on a loop. The radius of the first hill circular path is 8 meters and the velocity over this hill is 3m/s. The radius of the valley is 18 meters. The velocity at the bottom of the valley is 9m/s. What is the centripetal force at the top of the first hill? what is the normal force at the bottom of the valley? if the magnitude of normal force at the top of the hill 3200 what is the velocity? what is the total mechanical energy?

you have to draw the persons position over there

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.

b.a device that inputs heat into a cool object

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.