Newton's law of cooling says that the rate of cooling of an object is proportional to the difference between the temperature of the object and that of its surroundings (provided the difference is not too large). if t=t(t)t=t(t) represents the temperature of a (warm) object at time tt, aa represents the ambient (cool) temperature, and kk is a negative constant of proportionality, which equation(s) accurately characterize newton's law?

Explanation:

Newton's law of cooling

Rate of cooling

Where To is the surrounding temperature

T is object temperature at any time t

now by removing proportionality sign

Now by separating variables

So

Where C is constant

C' is also a constant and it can be find by using boundary conditions.

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.