Which object has the greatest kinetic energy?(1 point)

Question

Responses

a green car with a mass of 500kg moving at 21 m/s
a green car with a mass of 500kg moving at 21 m/s

a yellow car with a mass of 500 kg moving at 12 m/s
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 red car mass of 500 kg moving at 3 m/s

a blue car with a mass of 500 kg moving at 30 m/s
a blue car with a mass of 500 kg moving at 30 m/s

Answer 1

To determine which object has the greatest kinetic energy, we can use the formula for kinetic energy (KE):

\[ KE = \frac{1}{2}mv^2 \]

where \( m \) is the mass of the object and \( v \) is its speed.

Given that all the cars have the same mass (500 kg), we can simplify the comparison by focusing on the speed squared (\( v^2 \)).

Let's calculate the kinetic energy for each car:

1. Green Car:
   Mass = 500 kg, Speed = 21 m/s
   \[ KE = \frac{1}{2} \times 500 \times (21)^2 = \frac{1}{2} \times 500 \times 441 = 110250 \text{ J} \]

2. Yellow Car:
   Mass = 500 kg, Speed = 12 m/s
   \[ KE = \frac{1}{2} \times 500 \times (12)^2 = \frac{1}{2} \times 500 \times 144 = 36000 \text{ J} \]

3. Red Car:
   Mass = 500 kg, Speed = 3 m/s
   \[ KE = \frac{1}{2} \times 500 \times (3)^2 = \frac{1}{2} \times 500 \times 9 = 2250 \text{ J} \]

4. Blue Car:
   Mass = 500 kg, Speed = 30 m/s
   \[ KE = \frac{1}{2} \times 500 \times (30)^2 = \frac{1}{2} \times 500 \times 900 = 225000 \text{ J} \]

Now, comparing the kinetic energies:

• Green Car: 110250 J
• Yellow Car: 36000 J
• Red Car: 2250 J
• Blue Car: 225000 J

The blue car, having a speed of 30 m/s, has the greatest kinetic energy of 225000 J.