A bullet moving at 20m/sec. It strikes a wooden plank and penetrates 4 cm before coming to stop. The time taken to stop is

Options

A. 0.008 sec
B. 0.016 sec
C. 0.004 sec
D. 0.002 sec

Explanation

To solve the problem step by step, we will use the kinematic equations of motion. Here’s how we can determine the time taken for the bullet to stop after penetrating the wooden plank.

### Step 1: Identify the given values
- Initial velocity of the bullet (u) = 20 m/s
- Final velocity of the bullet (v) = 0 m/s (since it comes to a stop)
- Distance penetrated (s) = 4 cm = 0.04 m (convert centimeters to meters)

### Step 2: Use the kinematic equation
We will use the equation:
\[ v^2 = u^2 + 2as \]
where:
- v = final velocity
- u = initial velocity
- a = acceleration (which will be negative since it is deceleration)
- s = distance

### Step 3: Substitute the known values into the equation
Substituting the values we have:
\[ 0^2 = (20)^2 + 2a(0.04) \]
This simplifies to:
\[ 0 = 400 + 0.08a \]

### Step 4: Solve for acceleration (a)
Rearranging the equation to solve for a:
\[ 0.08a = -400 \]
\[ a = \frac{-400}{0.08} \]
\[ a = -5000 \, \text{m/s}^2 \]

### Step 5: Use another kinematic equation to find time (t)
Now we will use the equation:
\[ v = u + at \]
Substituting the known values:
\[ 0 = 20 + (-5000)t \]

### Step 6: Rearrange to solve for time (t)
Rearranging gives:
\[ 5000t = 20 \]
\[ t = \frac{20}{5000} \]
\[ t = 0.004 \, \text{seconds} \]

### Final Answer
The time taken for the bullet to stop is **0.004 seconds**.

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