A body of mass `(1)/(4) kg` moving with velocity `12 m//s` is stopped by applying a force of 0.6 N. Then impulse is :-

Options

A. 7.2 Ns
B. 3 Ns
C. 2.4 Ns
D. None

Answer

To solve the problem, we need to calculate the impulse experienced by the body. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Mass of the body, \( m = \frac{1}{4} \, \text{kg} \)
- Initial velocity, \( u = 12 \, \text{m/s} \)
- Final velocity, \( v = 0 \, \text{m/s} \) (since the body is stopped)
- Force applied, \( F = 0.6 \, \text{N} \)

### Step 2: Calculate the acceleration
Using Newton's second law, we can find the acceleration \( a \) of the body using the formula:
\[ F = m \cdot a \]
Rearranging gives:
\[ a = \frac{F}{m} \]
Substituting the values:
\[ a = \frac{0.6 \, \text{N}}{\frac{1}{4} \, \text{kg}} = 0.6 \times 4 = 2.4 \, \text{m/s}^2 \]

### Step 3: Calculate the time taken to stop
Using the equation of motion:
\[ v = u + at \]
We can rearrange to find the time \( t \):
\[ t = \frac{v - u}{a} \]
Substituting the values:
\[ t = \frac{0 - 12}{-2.4} = \frac{-12}{-2.4} = 5 \, \text{s} \]

### Step 4: Calculate the impulse
Impulse \( J \) is given by the formula:
\[ J = F \cdot t \]
Substituting the values:
\[ J = 0.6 \, \text{N} \times 5 \, \text{s} = 3 \, \text{N} \cdot \text{s} \]

### Final Answer
The impulse is \( 3 \, \text{N} \cdot \text{s} \).

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