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
