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 concept of velocity
Velocity is defined as the rate of change of displacement with respect to time. The standard unit of velocity is meters per second (m/s).

### Step 2: Determine the dimensions of velocity
The dimensions of velocity can be derived from its unit:
- Length (displacement) is measured in meters (m), which has the dimension [L].
- Time is measured in seconds (s), which has the dimension [T].

Thus, the dimension of velocity (v) can be expressed as:
\[ [v] = [L][T]^{-1} \]

### Step 3: Identify the change in velocity
The change in velocity (Δv) is defined as the difference between two velocities (v1 and v2):
\[ \Delta v = v_2 - v_1 \]

### Step 4: Determine the dimensions of the change in velocity
Since Δv is simply the difference between two velocities, the dimensions of Δv will be the same as the dimensions of velocity. Therefore:
\[ [\Delta v] = [v] = [L][T]^{-1} \]

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