The velocity of a bullet is reduced from `400 ms^(-1)` to `100 ms^(-1)` while travelling thought material of thickness of 1 m. The retardation will be

Options

A. `7.5 * 10^4 m/s^2`
B. `8.5 * 10^3 m/s^2`
C. `7.5 * 10^2 m/s^2`
D. `8.5 * 10^2 m/s^2`

Answer

To find the retardation of the bullet as it travels through the material, we can use the third equation of motion. Let's break down the solution step by step:

### Step 1: Identify the given values
- Initial velocity (u) = 400 m/s
- Final velocity (v) = 100 m/s
- Displacement (s) = 1 m

### Step 2: Write the third equation of motion
The third equation of motion is given by:
\[ v^2 = u^2 + 2as \]
where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration (which will be negative for retardation)
- \( s \) = displacement

### Step 3: Rearrange the equation to solve for acceleration (a)
We can rearrange the equation to find acceleration:
\[ a = \frac{v^2 - u^2}{2s} \]

### Step 4: Substitute the known values into the equation
Now, substitute the values of \( v \), \( u \), and \( s \):
\[ a = \frac{(100)^2 - (400)^2}{2 \times 1} \]

### Step 5: Calculate the squares
Calculate \( v^2 \) and \( u^2 \):
- \( v^2 = 100^2 = 10000 \)
- \( u^2 = 400^2 = 160000 \)

### Step 6: Substitute the squared values back into the equation
Now substitute these values back into the equation:
\[ a = \frac{10000 - 160000}{2 \times 1} \]
\[ a = \frac{-150000}{2} \]

### Step 7: Calculate the acceleration
Now perform the division:
\[ a = -75000 \, \text{m/s}^2 \]

### Step 8: Interpret the result
Since the acceleration is negative, this indicates that it is a retardation. Therefore, the retardation of the bullet is:
\[ \text{Retardation} = 75000 \, \text{m/s}^2 \]

### Final Answer
The retardation of the bullet is \( 75000 \, \text{m/s}^2 \).

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