Two identical masses are moving down a slope. One mass is traveling twice as fast as the other mass. How does the kinetic energy of one mass compare to the other?

a. The faster object has the same kinetic energy as the slower object.
b. The faster object has less kinetic energy than the slower object.
c. The faster object has twice as much kinetic energy as the slower object.
d. The faster object has four times as much kinetic energy as the slower object

To compare the kinetic energy of two objects, we can use the equation:

Kinetic Energy = (1/2) * mass * velocity^2

Let's assign some variables to the given information:
- Mass of both objects = m
- Velocity of slower object = v
- Velocity of faster object = 2v (twice as fast)

Now, let's calculate the kinetic energy for both objects.

For the slower object:
Kinetic Energy (slower) = (1/2) * m * v^2

For the faster object:
Kinetic Energy (faster) = (1/2) * m * (2v)^2 = (1/2) * m * 4v^2 = 2 * (1/2) * m * v^2

As we can see, the kinetic energy of the faster object is twice (2 * (1/2)) as much as the kinetic energy of the slower object.

Therefore, the answer is: c. The faster object has twice as much kinetic energy as the slower object.

To compare the kinetic energy of two objects, we use the formula for kinetic energy:

Kinetic Energy = (1/2) * mass * velocity^2

Both masses are identical, so let's call their mass "m". Let's also assume the velocity of the slower mass is "v" and the velocity of the faster mass is "2v".

Plugging these values into the formula, we can calculate the kinetic energy for each mass:

For the slower mass:
Kinetic Energy (Slower) = (1/2) * m * v^2

For the faster mass:
Kinetic Energy (Faster) = (1/2) * m * (2v)^2 = (1/2) * m * 4v^2

Simplifying the expression for the kinetic energy of the faster mass, we get:
Kinetic Energy (Faster) = 2 * (1/2) * m * v^2 = (1/2) * m * v^2

From this, we can conclude that the kinetic energy of the faster mass is equal to the kinetic energy of the slower mass. Thus, the answer is:

a. The faster object has the same kinetic energy as the slower object.

KE is dependent on the square of the velocity. twice^2 = 4times