A body of mass 6 kg is acted on a by a force so that its velocity changes from `3 ms^(-1)` to `5ms^(-1)`, then change in momentum is

Options

A. 48 Ns
B. 24 Ns
C. 30 Ns
D. 12 Ns

Explanation

To solve the problem of finding the change in momentum of a body with a mass of 6 kg that changes its velocity from 3 m/s to 5 m/s, we can follow these steps:

### Step 1: Understand the concept of momentum
Momentum (P) is defined as the product of mass (m) and velocity (v):
\[ P = m \times v \]

### Step 2: Identify the initial and final velocities
- Initial velocity (\(v_i\)) = 3 m/s
- Final velocity (\(v_f\)) = 5 m/s

### Step 3: Calculate the initial momentum
Using the formula for momentum:
\[ P_{\text{initial}} = m \times v_i \]
Substituting the values:
\[ P_{\text{initial}} = 6 \, \text{kg} \times 3 \, \text{m/s} = 18 \, \text{kg m/s} \]

### Step 4: Calculate the final momentum
Using the same formula for momentum:
\[ P_{\text{final}} = m \times v_f \]
Substituting the values:
\[ P_{\text{final}} = 6 \, \text{kg} \times 5 \, \text{m/s} = 30 \, \text{kg m/s} \]

### Step 5: Calculate the change in momentum
The change in momentum (\(\Delta P\)) is given by:
\[ \Delta P = P_{\text{final}} - P_{\text{initial}} \]
Substituting the values:
\[ \Delta P = 30 \, \text{kg m/s} - 18 \, \text{kg m/s} = 12 \, \text{kg m/s} \]

### Step 6: State the final answer
The change in momentum is:
\[ \Delta P = 12 \, \text{kg m/s} \]
or in Newton-seconds (since 1 kg m/s = 1 N·s):
\[ \Delta P = 12 \, \text{N·s} \]

### Final Answer:
The change in momentum is **12 N·s**.

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