Which car has the most kinetic energy?

A. A car of mass 1000 kg with speed 3 m/s

B. A car of mass 1000 kg with speed 7 m/s

C. A car of mass 2000 kg with speed 3 m/s

D. A car of mass 2000 kg with speed 7 m/s



Answer :

To determine which car has the most kinetic energy, we will use the kinetic energy formula:

[tex]\[ \text{Kinetic Energy} (KE) = \frac{1}{2} \times \text{mass} \times \text{velocity}^2 \][/tex]

We are given the following data for each car:

1. Car A:
- Mass: 1000 kg
- Speed: 3 m/s

2. Car B:
- Mass: 1000 kg
- Speed: 7 m/s

3. Car C:
- Mass: 2000 kg
- Speed: 3 m/s

4. Car D:
- Mass: 2000 kg
- Speed: 7 m/s

Let's calculate the kinetic energy for each car:

1. Kinetic energy of Car A:
[tex]\[ KE_1 = \frac{1}{2} \times 1000 \, \text{kg} \times (3 \, \text{m/s})^2 = 0.5 \times 1000 \times 9 = 4500 \, \text{J} \][/tex]

2. Kinetic energy of Car B:
[tex]\[ KE_2 = \frac{1}{2} \times 1000 \, \text{kg} \times (7 \, \text{m/s})^2 = 0.5 \times 1000 \times 49 = 24500 \, \text{J} \][/tex]

3. Kinetic energy of Car C:
[tex]\[ KE_3 = \frac{1}{2} \times 2000 \, \text{kg} \times (3 \, \text{m/s})^2 = 0.5 \times 2000 \times 9 = 9000 \, \text{J} \][/tex]

4. Kinetic energy of Car D:
[tex]\[ KE_4 = \frac{1}{2} \times 2000 \, \text{kg} \times (7 \, \text{m/s})^2 = 0.5 \times 2000 \times 49 = 49000 \, \text{J} \][/tex]

Now, we compare the kinetic energies:

- Car A: 4500 J
- Car B: 24500 J
- Car C: 9000 J
- Car D: 49000 J

Among these, the car with the most kinetic energy is Car D with 49000 J.

Therefore, the car with the most kinetic energy is:
- D. A car of mass 2000 kg with speed 7 m/s