You are told 3 things...1. That there are two objects with equal masses. 2. Both objects are in motion.

Question

You are told 3 things...1. That there are two objects with equal masses. 2. Both objects are in motion.
3. One object has a greater kinetic energy than the other. How is this possible? (1 point)
One object is blue and one object is red.
One object has a greater speed than the other object.
One object has a greater density then the other object.
One object has a greater volume than the other object.

GPT-4o mini · Answer

The situation described can happen when one object has a greater speed than the other object.

Kinetic energy ($KE$) is given by the formula:

\[ KE = \frac{1}{2} m v^2 \]

where $m$ is the mass of the object and $v$ is its speed. Since both objects have equal masses, the object with the higher speed will have a greater kinetic energy. The other factors mentioned (density and volume) do not directly affect kinetic energy in this context, since they do not change the mass or speed of the objects.

Answer

A large truck and a small car are moving at the same speed, traveling up and down hills, and over
bumpy roads. Which one has more kinetic energy?(1 point)
The car has more kinetic energy because it moves fast down hills.
The truck has less kinetic energy because it has greater mass.
The truck has more kinetic energy because it has a greater mass.
The car and truck have the same kinetic energy.

GPT-4o mini · Answer

The correct answer is: **The truck has more kinetic energy because it has a greater mass.** Kinetic energy is given by the formula: $$ KE = \frac{1}{2} m v^2 $$ where $m$ is the mass and $v$ is the speed of the object. Since both the truck and the car are moving at the same speed, the object with the greater mass (the truck) will have more kinetic energy.

Answer

Which object has the greatest kinetic energy?(1 point)
a yellow car with a mass of 500 kg moving at 12 m/s
a red car mass of 500 kg moving at 3 m/s
a green car with a mass of 500kg moving at 21 m/s
a blue car with a mass of 500 kg moving at 30 m/s

GPT-4o mini · Answer

To find which object has the greatest kinetic energy, we can use the kinetic energy formula:

\[ KE = \frac{1}{2} m v^2 \]

Since all the cars have the same mass (500 kg), we only need to consider their speeds to find the kinetic energy.

Yellow car: $ KE = \frac{1}{2} \times 500 , \text{kg} \times (12 , \text{m/s})^2 = \frac{1}{2} \times 500 \times 144 = 36000 , \text{J} $
Red car: $ KE = \frac{1}{2} \times 500 , \text{kg} \times (3 , \text{m/s})^2 = \frac{1}{2} \times 500 \times 9 = 2250 , \text{J} $
Green car: $ KE = \frac{1}{2} \times 500 , \text{kg} \times (21 , \text{m/s})^2 = \frac{1}{2} \times 500 \times 441 = 110250 , \text{J} $
Blue car: $ KE = \frac{1}{2} \times 500 , \text{kg} \times (30 , \text{m/s})^2 = \frac{1}{2} \times 500 \times 900 = 225000 , \text{J} $

Now comparing the kinetic energies:

Yellow car: 36,000 J
Red car: 2,250 J
Green car: 110,250 J
Blue car: 225,000 J

The blue car has the greatest kinetic energy at 225,000 joules.

Answer

A skydiver jumps out of a plane and begins to accelerate. His speed increases to 20 m/s, then 30 m/s.
His acceleration slows until he reaches a constant speed of 50 m/s. Which statement accurately
describes his kinetic energy while falling?(1 point)
His kinetic energy was positive at first, but it decreased to zero when he stopped accelerating.
His kinetic energy increased quickly at first, then it increased at a constant rate.
His kinetic energy increased while his speed increases, then it became constant.
His kinetic energy would remain the same for the whole fall as long as he lost no mass.

GPT-4o mini · Answer

The correct statement is: **His kinetic energy increased while his speed increases, then it became constant.** As the skydiver accelerates and his speed increases from 20 m/s to 30 m/s, his kinetic energy also increases. Kinetic energy is given by the formula: $$ KE = \frac{1}{2} m v^2 $$ Since his speed is increasing, his kinetic energy will increase as well. Once he reaches a constant speed of 50 m/s, his kinetic energy will become constant as well, provided his mass remains unchanged. So the correct choice effectively captures the changes in the skydiver's kinetic energy during the fall.