A body moving with some initial velocity and having uniform acceleration attains a final velocity v m/s after travelling x m. If its final velocity is v = `sqrt (180 - 7x)`, find the acceleration of the body.

Options

A. `- 3.5 m//s^(2)`
B. `-7m//s^(2)`
C. `-15 m//s^(2)`
D. `-30 m//s^(2)`

Explanation

To solve the problem step by step, we will follow the given information and apply the relevant equations of motion.

### Step 1: Write down the given equation for final velocity
We are given that the final velocity \( v \) is expressed as:
\[ v = \sqrt{180 - 7x} \]

### Step 2: Square both sides of the equation
To eliminate the square root, we square both sides:
\[ v^2 = 180 - 7x \]

### Step 3: Rearrange the equation
Rearranging the equation gives us:
\[ v^2 + 7x = 180 \]
This can be rewritten as:
\[ v^2 = 180 - 7x \]

### Step 4: Use the kinematic equation
We can use the kinematic equation that relates initial velocity \( u \), final velocity \( v \), acceleration \( a \), and distance \( x \):
\[ v^2 = u^2 + 2ax \]
We will compare this equation with our derived equation \( v^2 = 180 - 7x \).

### Step 5: Compare the two equations
From the two equations:
1. \( v^2 = 180 - 7x \)
2. \( v^2 = u^2 + 2ax \)

We can identify:
- \( u^2 = 180 \) (initial velocity squared)
- \( 2ax = -7x \)

### Step 6: Solve for acceleration \( a \)
From the equation \( 2ax = -7x \), we can divide both sides by \( x \) (assuming \( x \neq 0 \)):
\[ 2a = -7 \]
Now, solving for \( a \):
\[ a = -\frac{7}{2} = -3.5 \, \text{m/s}^2 \]

### Conclusion
The acceleration of the body is:
\[ a = -3.5 \, \text{m/s}^2 \]

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