Let displacement `S = t^(2) + 3t + 4`. Find initial velocity in S.I. unit.

Options

A. 0 m/s
B. 1 m/s
C. 2 m/s
D. 3 m/s

Explanation

To find the initial velocity from the given displacement equation \( S = t^2 + 3t + 4 \), we can follow these steps:

### Step-by-step Solution:

1. **Understand the relationship between displacement and velocity**:
- Velocity is defined as the rate of change of displacement with respect to time. Mathematically, this is expressed as:
\[ v = \frac{dS}{dt} \]

2. **Differentiate the displacement equation**:
- Given the displacement \( S = t^2 + 3t + 4 \), we need to differentiate this equation with respect to time \( t \):
\[ v = \frac{dS}{dt} = \frac{d}{dt}(t^2 + 3t + 4) \]

3. **Perform the differentiation**:
- Using the power rule of differentiation, we differentiate each term:
- The derivative of \( t^2 \) is \( 2t \).
- The derivative of \( 3t \) is \( 3 \).
- The derivative of the constant \( 4 \) is \( 0 \).
- Therefore, the velocity equation becomes:
\[ v = 2t + 3 \]

4. **Find the initial velocity**:
- The initial velocity is the velocity at time \( t = 0 \):
\[ v(0) = 2(0) + 3 = 3 \, \text{m/s} \]

5. **Conclusion**:
- The initial velocity is \( 3 \, \text{m/s} \).

### Final Answer:
The initial velocity in SI units is \( 3 \, \text{m/s} \).