When you are on a roller coaster, you are constantly transforming from Potential to Kinetic energy and back. Explain how these energy transformation would occur as the coaster goes from point A all the way to point E.

The two types of energy possessed by the roller coaster are:

- Potential energy: it is the energy possessed by the roller coaster due to its position. It is calculated as

where

m is the mass of the roller coaster

g is the acceleration due to gravity

h is the height of the roller coaster relative to the ground

- KInetic energy: it is the energy possessed by the roller coaster due to its motion. It is calculated as

where

v is the speed of the roller coaster

Moreover, according to the law of conservation of energy, the total mechanical energy of the roller coaster (the sum of potential+kinetic energy) is constant during the motion:

This implies that:

- When PE increases (because h increases), KE decreases (because v decreases)

- When PE decreases (because h decreases), KE increases (because v increases)

Now we can apply these conclusions to the motion of the roller coaster:

- When it moves from A to B, potential energy is converted into kinetic energy, so PE decreases and KE increases

- When it moves from B to C, kinetic energy is converted into potential energy, so PE increases and KE decreases

- When it moves from C to D, potential energy is converted into kinetic energy, so PE decreases and KE increases

- When it moves from D to E,  kinetic energy is converted into potential energy, so PE increases and KE decreases

the answer is c i did the same question so i know that's right!

answer: a) y=-8x+5

a) m= -8

b) m= -2

c) m= 7

d) m= 6