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 will follow these steps:

### Step 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:
\[ v = \frac{dS}{dt} \]
where \( v \) is the velocity and \( S \) is the displacement.

### Step 2: Differentiate the displacement function
Given the displacement function:
\[ S = t^2 + 3t + 4 \]
we need to differentiate this with respect to \( t \).

Using the rules of differentiation:
- The derivative of \( t^2 \) is \( 2t \).
- The derivative of \( 3t \) is \( 3 \).
- The derivative of a constant (4) is \( 0 \).

Thus, we can differentiate \( S \):
\[ \frac{dS}{dt} = 2t + 3 \]

### Step 3: Find the initial velocity
The initial velocity is the velocity at \( t = 0 \). We substitute \( t = 0 \) into the velocity equation:
\[ v = 2(0) + 3 = 3 \, \text{m/s} \]

### Conclusion
The initial velocity of the body is:
\[ \text{Initial Velocity} = 3 \, \text{m/s} \]

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