Help explaining physics

Question

Question: As the speed of a bicycle moving along a level horizontal surface changes from 2 m/s to 4 m/s, the magnitude of the bicycle's:

 

Multiple Choice:

a. total energy remains the same

b. kinetic energy decreases

c. gravitational potential energy remains the same

d. kinetic energy remains the same

 

Answer: c. gravitational potential energy remains the same

 

Please explain why this answer is correct, explain fully using physics terms. As well as explain why the other answers don't work.

Answer 1

The total energy of the bicycle is equal to the gravitational energy and kinetic energy.

First velocity:

energy = E(grav) + kE

energy = mgh + 1/2 mv^2

energy = mgh + 1/2 m(2)^2

energy = mgh + 2m

 

second velocity:

energy = mgh + 1/2 mv^2
energy = mgh + 1/2 m(4)^2
energy = mgh + 8m

 

as can be seen the KE has increased by 4 times so:

a is not correct

b is not correct

c is correct (this would change only if there was a difference in height)

d is not correct

 

 

 

Answer 2

Gravitational energy would act in a vertical direction, but it's impeded by the solidity of the horizontal bicycle path--but it remains the same.  But kinetic energy is increasing.