If the unit of length is micrometer and the unit of time is microsecond, the unit of velcoity will be :

Options

A. `100 m//s`
B. `10m//s`
C. micrometers
D. `m//s`

Answer

To determine the unit of velocity when the unit of length is micrometer and the unit of time is microsecond, we can follow these steps:

### Step 1: Understand the Units
- The unit of length is given as micrometer (µm).
- The unit of time is given as microsecond (µs).

### Step 2: Convert the Units to Standard SI Units
- 1 micrometer (µm) = \(10^{-6}\) meters (m)
- 1 microsecond (µs) = \(10^{-6}\) seconds (s)

### Step 3: Write the Formula for Velocity
Velocity (v) is defined as the ratio of length (distance) to time:
\[ v = \frac{\text{length}}{\text{time}} \]

### Step 4: Substitute the Units into the Formula
Substituting the conversions into the velocity formula:
\[ v = \frac{10^{-6} \text{ m}}{10^{-6} \text{ s}} \]

### Step 5: Simplify the Expression
When we simplify the expression, the \(10^{-6}\) in the numerator and denominator cancels out:
\[ v = \frac{10^{-6} \text{ m}}{10^{-6} \text{ s}} = \frac{\text{m}}{\text{s}} \]

### Step 6: State the Unit of Velocity
Thus, the unit of velocity is meters per second (m/s).

### Final Answer
The unit of velocity is **meters per second (m/s)**.

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