The speed of a motor car becomes six times, then the kinetic energy becomes

Options

A. 6 times
B. 36 times
C. 12 times
D. 24 times

Answer

To solve the problem, we need to understand the relationship between the speed of an object and its kinetic energy. The formula for kinetic energy (KE) is given by:

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

where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass of the object,
- \( v \) is the speed of the object.

### Step-by-Step Solution:

1. **Identify the initial kinetic energy**:
- Let the initial speed of the motor car be \( v \).
- The initial kinetic energy \( KE_1 \) can be expressed as:
\[ KE_1 = \frac{1}{2} mv^2 \]

2. **Determine the new speed**:
- According to the problem, the speed of the motor car becomes six times the original speed. Therefore, the new speed \( v' \) is:
\[ v' = 6v \]

3. **Calculate the new kinetic energy**:
- The new kinetic energy \( KE_2 \) when the speed is \( 6v \) can be calculated as:
\[ KE_2 = \frac{1}{2} m (6v)^2 \]
- Simplifying this gives:
\[ KE_2 = \frac{1}{2} m (36v^2) = 18mv^2 \]

4. **Relate the new kinetic energy to the initial kinetic energy**:
- We can express \( KE_2 \) in terms of \( KE_1 \):
\[ KE_2 = 36 \left(\frac{1}{2} mv^2\right) = 36 KE_1 \]

5. **Conclusion**:
- Therefore, when the speed of the motor car increases to six times its original speed, the kinetic energy becomes 36 times the initial kinetic energy.

### Final Answer:
The kinetic energy becomes **36 times**.

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