What are the dimensions of the change in velocity ?

Options

A. `[M^0L^0T^0]`
B. `[LT^(-1)]`
C. `[MLT^(-1)]`
D. `[LT^(-2)]`

Answer

To find the dimensions of the change in velocity, we can follow these steps:

### Step 1: Understand the Definition of Velocity
Velocity is defined as the rate of change of displacement with respect to time. Mathematically, it can be expressed as:
\[ \text{Velocity} = \frac{\text{Displacement}}{\text{Time}} \]

### Step 2: Identify the Dimensions of Displacement and Time
- The dimension of displacement (which is a measure of length) is represented as \( [L] \).
- The dimension of time is represented as \( [T] \).

### Step 3: Write the Dimensions of Velocity
From the definition, we can express the dimensions of velocity as:
\[ [\text{Velocity}] = \frac{[L]}{[T]} = [L][T]^{-1} \]

### Step 4: Understand Change in Velocity
The change in velocity refers to the difference in velocity over a certain time interval. However, the dimensions of change in velocity will remain the same as that of velocity itself because it is still a measure of how fast something is moving.

### Step 5: Write the Dimensions of Change in Velocity
Thus, the dimensions of change in velocity are:
\[ [\text{Change in Velocity}] = [L][T]^{-1} \]

### Conclusion
The dimensions of the change in velocity are:
\[ [L][T]^{-1} \]

### Final Answer
The dimensions of the change in velocity are \( L^1 T^{-1} \).

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