The ratio of unit of acceleration and velocity gives unit of the physical quantity

Options

A. time
B. frequency
C. amplitude
D. speed

Explanation

To solve the problem, we need to find out what physical quantity is represented by the ratio of the units of acceleration and velocity.

### Step-by-Step Solution:

1. **Identify the Units of Acceleration and Velocity**:
- The unit of **acceleration** is defined as the rate of change of velocity. It is given by:
\[ \text{Acceleration} = \frac{\text{Change in Velocity}}{\text{Time}} = \frac{m/s}{s} = \frac{m}{s^2} \]
- The unit of **velocity** is defined as the rate of change of displacement. It is given by:
\[ \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} = \frac{m}{s} \]

2. **Formulate the Ratio**:
- Now, we take the ratio of the unit of acceleration to the unit of velocity:
\[ \text{Ratio} = \frac{\text{Unit of Acceleration}}{\text{Unit of Velocity}} = \frac{m/s^2}{m/s} \]

3. **Simplify the Ratio**:
- When we simplify this ratio, the meters (m) cancel out:
\[ \text{Ratio} = \frac{1}{s^2} \times s = \frac{1}{s} = s^{-1} \]

4. **Identify the Physical Quantity**:
- The unit \( s^{-1} \) is the same as the unit of **frequency**. Frequency is defined as the number of occurrences of a repeating event per unit time, and its unit is Hertz (Hz), which is equivalent to \( s^{-1} \).

5. **Conclusion**:
- Therefore, the ratio of the unit of acceleration and velocity gives us the unit of **frequency**.

### Final Answer:
The physical quantity represented by the ratio of the units of acceleration and velocity is **frequency**.

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