A body of mass 5 kg is moving with velocity of `v=(2hati+6hatj)ms^(-1)` at t=0s. After time t=2s, velocity of body is `(10 hati+6 hatj)`, then change in momentum to body is

Options

A. `40 hati kgms^(-1)`
B. `20hati kgms^(-1)`
C. `30 hati kgms^(-1)`
D. `(50 hati+30 hatj)kgms^(-1)`

Explanation

To find the change in momentum of the body, we can follow these steps:

### Step 1: Identify the given values
- Mass of the body, \( m = 5 \, \text{kg} \)
- Initial velocity at \( t = 0 \, \text{s} \), \( \mathbf{u} = 2 \hat{i} + 6 \hat{j} \, \text{m/s} \)
- Final velocity at \( t = 2 \, \text{s} \), \( \mathbf{v} = 10 \hat{i} + 6 \hat{j} \, \text{m/s} \)

### Step 2: Calculate the change in velocity
The change in velocity \( \Delta \mathbf{v} \) can be calculated using the formula:
\[ \Delta \mathbf{v} = \mathbf{v} - \mathbf{u} \]
Substituting the values:
\[ \Delta \mathbf{v} = (10 \hat{i} + 6 \hat{j}) - (2 \hat{i} + 6 \hat{j}) \]
Now, simplify this:
\[ \Delta \mathbf{v} = (10 - 2) \hat{i} + (6 - 6) \hat{j} = 8 \hat{i} + 0 \hat{j} \]
So, \( \Delta \mathbf{v} = 8 \hat{i} \, \text{m/s} \).

### Step 3: Calculate the change in momentum
The change in momentum \( \Delta \mathbf{p} \) is given by:
\[ \Delta \mathbf{p} = m \cdot \Delta \mathbf{v} \]
Substituting the values:
\[ \Delta \mathbf{p} = 5 \, \text{kg} \cdot (8 \hat{i} \, \text{m/s}) = 40 \hat{i} \, \text{kg m/s} \]

### Final Answer
The change in momentum of the body is:
\[ \Delta \mathbf{p} = 40 \hat{i} \, \text{kg m/s} \]

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