If a roller-coaster car has 40,000 J of gravitational potential energy when at rest on the top of a hill, how much kinetic energy does it have when it is ½ of the way down the hill?

Work Shown:

PE = potential energy

KE = kinetic energy

m = mass

g = acceleration of gravity

h = height of the object

PE = m*g*h = 40,000 joules

If the car is halfway down the hill, then that means the height of the car is h/2 instead of h

We can then say:

m*g*(h/2) = (m*g*h)/2 = (40,000)/2 = 20,000 J

is the amount of potential energy at this location. The amount of kinetic energy must be the remaining amount that adds to this, to get 40,000 J again.

Put another way: The 40,000 J of PE to start off with, when KE = 0, means we have a total energy of 40,000 J

So,

PE+KE = total energy

PE+KE = 40,000 J

20,000 J + KE = 40,000 J

KE = (40,000 J) - (20,000 J)

KE = 20,000 J when the car is halfway down the hill.

a=d/t

a="triangle"v/t

explanation:

a = acceleration

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.