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Answer :
To find the kinetic energy of the car, we can follow these steps:
1. Identify the Information Given:
- The mass of the car is 1200 kg.
- The momentum of the car is 18000 kg·m/s.
2. Understanding the Concepts:
- Momentum is the product of mass and velocity. It's given as:
[tex]\[
\text{momentum} = \text{mass} \times \text{velocity}
\][/tex]
- Kinetic energy (KE) is calculated using:
[tex]\[
\text{KE} = \frac{1}{2} \times \text{mass} \times \text{velocity}^2
\][/tex]
3. Calculate the Velocity:
- Use the momentum formula to find the velocity:
[tex]\[
\text{velocity} = \frac{\text{momentum}}{\text{mass}} = \frac{18000 \, \text{kg·m/s}}{1200 \, \text{kg}} = 15 \, \text{m/s}
\][/tex]
4. Calculate the Kinetic Energy:
- Substitute the values into the kinetic energy formula:
[tex]\[
\text{KE} = \frac{1}{2} \times 1200 \, \text{kg} \times (15 \, \text{m/s})^2
\][/tex]
- Simplify the calculation:
[tex]\[
\text{KE} = \frac{1}{2} \times 1200 \times 225
\][/tex]
[tex]\[
\text{KE} = 600 \times 225 = 135000 \, \text{Joules}
\][/tex]
5. Convert Joules to Kilojoules:
- Since 1 kilojoule (kJ) is 1000 joules (J), convert the energy:
[tex]\[
\text{KE} = \frac{135000 \, \text{J}}{1000} = 135 \, \text{kJ}
\][/tex]
From the calculations, the kinetic energy of the car is 135 kJ. Therefore, the correct option is C 135 kJ.
1. Identify the Information Given:
- The mass of the car is 1200 kg.
- The momentum of the car is 18000 kg·m/s.
2. Understanding the Concepts:
- Momentum is the product of mass and velocity. It's given as:
[tex]\[
\text{momentum} = \text{mass} \times \text{velocity}
\][/tex]
- Kinetic energy (KE) is calculated using:
[tex]\[
\text{KE} = \frac{1}{2} \times \text{mass} \times \text{velocity}^2
\][/tex]
3. Calculate the Velocity:
- Use the momentum formula to find the velocity:
[tex]\[
\text{velocity} = \frac{\text{momentum}}{\text{mass}} = \frac{18000 \, \text{kg·m/s}}{1200 \, \text{kg}} = 15 \, \text{m/s}
\][/tex]
4. Calculate the Kinetic Energy:
- Substitute the values into the kinetic energy formula:
[tex]\[
\text{KE} = \frac{1}{2} \times 1200 \, \text{kg} \times (15 \, \text{m/s})^2
\][/tex]
- Simplify the calculation:
[tex]\[
\text{KE} = \frac{1}{2} \times 1200 \times 225
\][/tex]
[tex]\[
\text{KE} = 600 \times 225 = 135000 \, \text{Joules}
\][/tex]
5. Convert Joules to Kilojoules:
- Since 1 kilojoule (kJ) is 1000 joules (J), convert the energy:
[tex]\[
\text{KE} = \frac{135000 \, \text{J}}{1000} = 135 \, \text{kJ}
\][/tex]
From the calculations, the kinetic energy of the car is 135 kJ. Therefore, the correct option is C 135 kJ.
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