A bullet emerges from a barrel of length `1.2 m` with a speed of `640 ms^(1)`. Assuming constant acceleration, after the gun is fired is

Options

A. 4m
B. 40m
C. 400us
D. 1s

Explanation

To solve the problem of a bullet emerging from a barrel with a given length and speed, we will use the equations of motion. Here’s a step-by-step solution:

### Step 1: Identify the Given Values
- Length of the barrel (s) = 1.2 m
- Final speed of the bullet (v) = 640 m/s
- Initial speed of the bullet (u) = 0 m/s (since the bullet starts from rest)

### Step 2: Use the Equation of Motion
We will use the equation of motion that relates initial velocity, final velocity, acceleration, and distance:
\[ v^2 = u^2 + 2as \]

### Step 3: Substitute the Known Values
Substituting the known values into the equation:
\[ (640)^2 = (0)^2 + 2a(1.2) \]

### Step 4: Simplify the Equation
This simplifies to:
\[ 640^2 = 2a(1.2) \]
\[ 409600 = 2.4a \]

### Step 5: Solve for Acceleration (a)
Now, we can solve for acceleration (a):
\[ a = \frac{409600}{2.4} \]
\[ a = 170666.67 \, \text{m/s}^2 \]

### Step 6: Calculate the Time Taken (t)
Now we can find the time taken for the bullet to travel through the barrel using the formula:
\[ v = u + at \]
Since \( u = 0 \):
\[ 640 = 0 + (170666.67)t \]
\[ t = \frac{640}{170666.67} \]
\[ t \approx 0.00375 \, \text{s} \]
\[ t \approx 3.75 \, \text{ms} \]

### Step 7: Final Answer
The time taken for the bullet to emerge from the barrel is approximately **3.75 milliseconds**.

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