If velocity of a particle is given by `v=(2t+3)m//s`. Then average velocity in interval `0letle1` s is :

Options

A. `(7)/(2)m//s`
B. `(9)/(2) m//s`
C. `4 m//s`
D. `5 m//s`

Explanation

To find the average velocity of a particle over the time interval from \( t = 0 \) to \( t = 1 \) seconds, we can follow these steps:

### Step 1: Understand the formula for average velocity
The average velocity \( V_{avg} \) over a time interval can be calculated using the formula:
\[ V_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}} \]
In terms of integration, this can be expressed as:
\[ V_{avg} = \frac{1}{T} \int_{0}^{T} v(t) \, dt \]
where \( T \) is the total time interval.

### Step 2: Identify the velocity function
The velocity of the particle is given by:
\[ v(t) = 2t + 3 \, \text{m/s} \]

### Step 3: Set up the integral for displacement
We need to calculate the integral of the velocity function from \( t = 0 \) to \( t = 1 \):
\[ \int_{0}^{1} (2t + 3) \, dt \]

### Step 4: Calculate the integral
To compute the integral, we find:
\[ \int (2t + 3) \, dt = t^2 + 3t + C \]
Now, we evaluate this from \( 0 \) to \( 1 \):
\[ \left[ t^2 + 3t \right]_{0}^{1} = (1^2 + 3 \cdot 1) - (0^2 + 3 \cdot 0) = (1 + 3) - (0) = 4 \]

### Step 5: Calculate the total time
The total time \( T \) for the interval from \( 0 \) to \( 1 \) is:
\[ T = 1 - 0 = 1 \, \text{s} \]

### Step 6: Calculate the average velocity
Now, we can calculate the average velocity:
\[ V_{avg} = \frac{\text{Total Displacement}}{\text{Total Time}} = \frac{4}{1} = 4 \, \text{m/s} \]

### Final Answer
Thus, the average velocity of the particle in the interval from \( 0 \) to \( 1 \) seconds is:
\[ \boxed{4 \, \text{m/s}} \]