Depicts the potential energy of a 400-kg pallet that slides from rest down a frictionless roller conveyer ramp, then moves across a frictionless horizontal conveyer, and finally encounters a horizontal spring at x=4.0m. When the pallet encounters the spring, it momentarily comes to rest at x=6.0m. A) What is the force constant of the spring? B) At what height h above the horizontal conveyer did the pallet begin sliding from rest?

C) What is the angle of inclination of the conveyer ramp?

D) What will be the speed of the pallet at x=6.0m if it begins sliding from rest at x=0?

Please provide explanations along with answers. I do not understand where to begin. Thank you so much.

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.

energy stored in the capacitor= 9.72 x 10⁻⁴ j

explanation:

the energy stored in the capacitor is given by

e= 1/2 c v²

e= energy stored

c= capacitance= 1.5 µc= 1.5 x 10⁻⁶f

v= potential difference=36 v

so energy stored= e= 1/2 (1.5 x 10⁻⁶) (36)²

energy stored= 9.72 x 10⁻⁴j