If a body starts from rest and travels 120 cm in the 6 second then what is the acceleration

Options

A. `0.20 ms^(-2)`
B. `0.027 ms^(-2)`
C. `0.218 ms^(-2)`
D. `0.03 ms^(-2)`

Explanation

To find the acceleration of a body that starts from rest and travels 120 cm in 6 seconds, we can use the formula for displacement during the nth second of motion. Here’s how to solve the problem step by step:

### Step 1: Convert the displacement from centimeters to meters
The displacement given is 120 cm. We need to convert this to meters for consistency in SI units.

\[ \text{Displacement} = 120 \, \text{cm} = \frac{120}{100} \, \text{m} = 1.2 \, \text{m} \]

### Step 2: Identify the parameters
- Initial velocity \( u = 0 \) (since the body starts from rest)
- Displacement in the 6th second \( s_n = 1.2 \, \text{m} \)
- The time \( n = 6 \) seconds

### Step 3: Use the formula for displacement in the nth second
The formula for displacement during the nth second is given by:

\[ s_n = u + \frac{a}{2} (2n - 1) \]

Substituting the known values into the formula:

\[ 1.2 = 0 + \frac{a}{2} (2 \times 6 - 1) \]

### Step 4: Simplify the equation
Calculate \( 2n - 1 \):

\[ 2 \times 6 - 1 = 12 - 1 = 11 \]

Now substitute this back into the equation:

\[ 1.2 = \frac{a}{2} \times 11 \]

### Step 5: Solve for acceleration \( a \)
Multiply both sides by 2 to eliminate the fraction:

\[ 2 \times 1.2 = a \times 11 \]

\[ 2.4 = 11a \]

Now, divide both sides by 11 to solve for \( a \):

\[ a = \frac{2.4}{11} \]

### Step 6: Calculate the value of acceleration
Now perform the division:

\[ a \approx 0.218 \, \text{m/s}^2 \]

### Final Answer
The acceleration of the body is approximately \( 0.218 \, \text{m/s}^2 \).

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