Ahypothetical planet has a mass of 1.66 times that of earth, but the same radius. what is gravitiy near its surface?

Explanation:

The gravitational acceleration on the surface of the earth is

where G is the universal gravitational constant, is the mass of earth, and is the radius of earth,

in general for any object the gravitational acceleration or gravity on its surface is:

in this case we know that the mass is 1.66 times the mass of earth:

and the radius is the same as for earth:

so the gravity for this planet is

which can be written in the following form:

where we know that , so:

and the acceleration of gravity on earth is:

so the acceleration or gravity on the planet is:

e/c, where e is its total energy

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.