If the unit of length is 16m and that of velocity is `24ms^(-1)`, the unit of time is (in second)

Options

A. `2//3`
B. `4//3`
C. `3//2`
D. 24

Answer

To solve the problem, we need to find the unit of time given the unit of length and the unit of velocity.

### Step-by-Step Solution:

1. **Understand the relationship between distance, velocity, and time**:
The fundamental equation that relates these quantities is:
\[ \text{Distance} = \text{Velocity} \times \text{Time} \]
Rearranging this equation to find time gives us:
\[ \text{Time} = \frac{\text{Distance}}{\text{Velocity}} \]

2. **Identify the given values**:
- The unit of length (distance) is given as \(16 \, \text{m}\).
- The unit of velocity is given as \(24 \, \text{m/s}\).

3. **Substitute the values into the formula**:
Using the formula for time:
\[ \text{Time} = \frac{\text{Length}}{\text{Velocity}} = \frac{16 \, \text{m}}{24 \, \text{m/s}} \]

4. **Simplify the expression**:
When we divide \(16 \, \text{m}\) by \(24 \, \text{m/s}\), we can simplify it as follows:
\[ \text{Time} = \frac{16}{24} \, \text{s} \]
This can be further simplified:
\[ \text{Time} = \frac{2}{3} \, \text{s} \]

5. **Conclusion**:
Therefore, the unit of time is:
\[ \text{Time} = \frac{2}{3} \, \text{seconds} \]

### Final Answer:
The unit of time is \(\frac{2}{3}\) seconds.

---