A body covers `4.9m, 14.7 m, 24.5 m and 34.3m` in the successive seconds of motion. The acceleration of the body is

Options

A. `2.7 ms ^(-2)`
B. `4.9 ms ^(-2)`
C. `9.8 ms ^(-2)`
D. `19.6 ms ^(-2)`

Answer

To find the acceleration of the body given the distances covered in successive seconds, we can use the equations of motion. Let's break down the solution step by step.

### Step 1: Understand the distances covered
The distances covered in successive seconds are:
- \( S_1 = 4.9 \, \text{m} \) (1st second)
- \( S_2 = 14.7 \, \text{m} \) (2nd second)
- \( S_3 = 24.5 \, \text{m} \) (3rd second)
- \( S_4 = 34.3 \, \text{m} \) (4th second)

### Step 2: Use the equation of motion
The distance covered in the nth second is given by the formula:
\[ S_n = u + \frac{a}{2}(2n - 1) \]
where \( S_n \) is the distance covered in the nth second, \( u \) is the initial velocity, \( a \) is the acceleration, and \( n \) is the time in seconds.

### Step 3: Set up equations for each second
For each second, we can set up the following equations:

1. For \( n = 1 \):
\[ S_1 = u + \frac{a}{2}(2 \cdot 1 - 1) = u + \frac{a}{2} \quad \text{(1)} \]
\[ 4.9 = u + \frac{a}{2} \]

2. For \( n = 2 \):
\[ S_2 = u + \frac{a}{2}(2 \cdot 2 - 1) = u + \frac{3a}{2} \quad \text{(2)} \]
\[ 14.7 = u + \frac{3a}{2} \]

3. For \( n = 3 \):
\[ S_3 = u + \frac{a}{2}(2 \cdot 3 - 1) = u + \frac{5a}{2} \quad \text{(3)} \]
\[ 24.5 = u + \frac{5a}{2} \]

4. For \( n = 4 \):
\[ S_4 = u + \frac{a}{2}(2 \cdot 4 - 1) = u + \frac{7a}{2} \quad \text{(4)} \]
\[ 34.3 = u + \frac{7a}{2} \]

### Step 4: Solve the equations
From equations (1) and (2):
\[ 14.7 - 4.9 = \left(u + \frac{3a}{2}\right) - \left(u + \frac{a}{2}\right) \]
\[ 9.8 = a \quad \text{(5)} \]

Now, we can verify this with the other equations.

From equations (2) and (3):
\[ 24.5 - 14.7 = \left(u + \frac{5a}{2}\right) - \left(u + \frac{3a}{2}\right) \]
\[ 9.8 = a \quad \text{(6)} \]

From equations (3) and (4):
\[ 34.3 - 24.5 = \left(u + \frac{7a}{2}\right) - \left(u + \frac{5a}{2}\right) \]
\[ 9.8 = a \quad \text{(7)} \]

### Conclusion
The acceleration \( a \) of the body is \( 9.8 \, \text{m/s}^2 \).