The average velocity of a body moving with uniform acceleration after travelling a distance of `3.06 m` is `0.34 m s^(-1)`. If the change in velocity of the body is `0.18 ms^(-1)` during this time, its uniform acceleration is .

Options

A. `0.01 m s^(-2)`
B. `0.02 m s^(-2)`
C. `0.013 m s^(-2)`
D. `0.04 m s^(-2)`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the given information
- Distance traveled (S) = 3.06 m
- Average velocity (V_avg) = 0.34 m/s
- Change in velocity (ΔV) = 0.18 m/s

### Step 2: Relate average velocity to initial and final velocity
The average velocity for uniformly accelerated motion can be expressed as:
\[ V_{avg} = \frac{U + V}{2} \]
where U is the initial velocity and V is the final velocity.

### Step 3: Express final velocity in terms of initial velocity
From the change in velocity, we know:
\[ \Delta V = V - U = 0.18 \quad \Rightarrow \quad V = U + 0.18 \]

### Step 4: Substitute final velocity in the average velocity equation
Substituting \(V\) in the average velocity equation:
\[ 0.34 = \frac{U + (U + 0.18)}{2} \]
This simplifies to:
\[ 0.34 = \frac{2U + 0.18}{2} \]
Multiplying both sides by 2:
\[ 0.68 = 2U + 0.18 \]
Now, isolate \(2U\):
\[ 2U = 0.68 - 0.18 = 0.50 \quad \Rightarrow \quad U = \frac{0.50}{2} = 0.25 \, \text{m/s} \]

### Step 5: Find final velocity
Now, substitute \(U\) back to find \(V\):
\[ V = U + 0.18 = 0.25 + 0.18 = 0.43 \, \text{m/s} \]

### Step 6: Use the kinematic equation to find acceleration
We will use the kinematic equation:
\[ V^2 = U^2 + 2AS \]
Rearranging for acceleration \(A\):
\[ A = \frac{V^2 - U^2}{2S} \]

### Step 7: Substitute the values into the equation
Substituting \(V = 0.43 \, \text{m/s}\), \(U = 0.25 \, \text{m/s}\), and \(S = 3.06 \, \text{m}\):
\[ A = \frac{(0.43)^2 - (0.25)^2}{2 \times 3.06} \]

### Step 8: Calculate the squares
Calculating the squares:
\[ (0.43)^2 = 0.1849 \quad \text{and} \quad (0.25)^2 = 0.0625 \]
Now substitute these values:
\[ A = \frac{0.1849 - 0.0625}{2 \times 3.06} = \frac{0.1224}{6.12} \]

### Step 9: Calculate acceleration
Now, divide:
\[ A \approx 0.0200 \, \text{m/s}^2 \]

### Final Answer
The uniform acceleration of the body is approximately \(0.0200 \, \text{m/s}^2\).

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