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 under constant acceleration. Here’s a step-by-step solution:

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

### Step 2: Use the third equation of motion
The third equation of motion relates the final velocity, initial velocity, acceleration, and displacement:
\[ v^2 = u^2 + 2as \]
Where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration
- \( s \) = displacement (length of the barrel)

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

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

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

### Step 6: Use the first equation of motion to find time (t)
Now we can use the first equation of motion to find the time taken for the bullet to travel through the barrel:
\[ v = u + at \]
Since \( u = 0 \):
\[ 640 = 0 + (170666.67)t \]
\[ t = \frac{640}{170666.67} \]
\[ t \approx 0.00374 \, \text{s} \]

### Step 7: Convert time to milliseconds
To convert seconds to milliseconds:
\[ t \approx 0.00374 \, \text{s} \times 1000 \, \text{ms/s} \]
\[ t \approx 3.74 \, \text{ms} \]

### Final Answer
The time taken for the bullet to travel through the barrel is approximately **3.74 milliseconds**.

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