A bullet fired from a gun experiences a force of `600 -2 xx 10^(5)` t in the barrel of the gun. Here t is in second . The force becomes zero as soon as the bullet leaves the barrel of the gun . The time for which the bullet was in the barrel of the gun is

Options

A. ` 2 xx 10^(-5)`s
B. ` 10^(-5)s`
C. ` 3 xx 10^(-5)`
D. ` 3 xx 10^(-3)`s

Answer

To solve the problem, we need to determine the time for which the bullet was in the barrel of the gun, given the force acting on it.

### Step-by-step Solution:

1. **Understand the Given Force Equation**:
The force \( F \) acting on the bullet is given by the equation:
\[ F = 600 - 2 \times 10^5 t \]
where \( t \) is the time in seconds.

2. **Set the Force to Zero**:
According to the problem, the force becomes zero as soon as the bullet leaves the barrel. Therefore, we can set the force equation to zero:
\[ 0 = 600 - 2 \times 10^5 t \]

3. **Rearrange the Equation**:
To find \( t \), we rearrange the equation:
\[ 2 \times 10^5 t = 600 \]

4. **Solve for \( t \)**:
Now, divide both sides by \( 2 \times 10^5 \):
\[ t = \frac{600}{2 \times 10^5} \]

5. **Calculate \( t \)**:
Simplifying the right side:
\[ t = \frac{600}{2} \times 10^{-5} = 300 \times 10^{-5} = 3 \times 10^{-3} \text{ seconds} \]

6. **Convert to Milliseconds**:
Since \( 1 \text{ second} = 1000 \text{ milliseconds} \):
\[ t = 3 \text{ milliseconds} \]

### Final Answer:
The time for which the bullet was in the barrel of the gun is \( 3 \text{ ms} \) or \( 3 \times 10^{-3} \text{ seconds} \).

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