If `S_(n)=2+0.4n` find initial velocity and acceleration

Options

A. `2.2` units. `0.4` units
B. 2.1 units, 0.3 units
C. 1.2 units, 0.4 units
D. 2.2 units, 0.3 units

Explanation

To solve the problem, we need to find the initial velocity (u) and acceleration (a) given the displacement in the nth second, represented by the equation \( S_n = 2 + 0.4n \).

### Step-by-Step Solution:

1. **Understand the given equation**:
The equation \( S_n = 2 + 0.4n \) represents the displacement in the nth second.

2. **Use the formula for displacement in nth second**:
The formula for displacement in the nth second is given by:
\[ S_n = u + a \left(n - \frac{1}{2}\right) \]
where \( u \) is the initial velocity and \( a \) is the acceleration.

3. **Set up the equation**:
We can equate the two expressions for \( S_n \):
\[ u + a \left(n - \frac{1}{2}\right) = 2 + 0.4n \]

4. **Expand the left side**:
Expanding the left side gives:
\[ u + an - \frac{a}{2} = 2 + 0.4n \]

5. **Group the terms**:
Rearranging the equation, we can group the terms involving \( n \) and the constant terms:
\[ an - 0.4n = 2 + \frac{a}{2} - u \]

6. **Compare coefficients**:
From the equation, we can compare the coefficients of \( n \) and the constant terms:
- For \( n \):
\[ a = 0.4 \]
- For the constant terms:
\[ u - \frac{a}{2} = 2 \]

7. **Substitute the value of \( a \)**:
Substitute \( a = 0.4 \) into the constant term equation:
\[ u - \frac{0.4}{2} = 2 \]
This simplifies to:
\[ u - 0.2 = 2 \]

8. **Solve for \( u \)**:
Adding \( 0.2 \) to both sides gives:
\[ u = 2 + 0.2 = 2.2 \]

### Final Results:
- Initial velocity \( u = 2.2 \) units
- Acceleration \( a = 0.4 \) units