If 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 of how the kinetic energy changes when the speed of a motor car increases six times, we can follow these steps:

### Step-by-Step Solution

1. **Understand the formula for kinetic energy (KE)**:
The kinetic energy of an object is given by the formula:
\[ KE = \frac{1}{2} m v^2 \]
where \( m \) is the mass of the object and \( v \) is its velocity.

2. **Identify the change in speed**:
According to the problem, the speed of the motor car becomes six times its original speed. If we denote the original speed as \( v \), the new speed can be expressed as:
\[ v' = 6v \]

3. **Substitute the new speed into the kinetic energy formula**:
Now, we can calculate the new kinetic energy (\( KE' \)) using the new speed:
\[ KE' = \frac{1}{2} m (v')^2 = \frac{1}{2} m (6v)^2 \]

4. **Simplify the expression**:
Expanding the equation gives:
\[ KE' = \frac{1}{2} m (36v^2) = 36 \left(\frac{1}{2} m v^2\right) \]
This shows that the new kinetic energy is 36 times the original kinetic energy.

5. **Conclusion**:
Therefore, if the speed of the motor car becomes six times, the kinetic energy becomes:
\[ KE' = 36 \times KE \]
The correct answer is that the kinetic energy becomes **36 times**.

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

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