Assertion : A body of mass 4 kg has an initial velocity `5hat(i)ms^(-1)`. It is subjected to a force of `4hat(j)N`. The displacement of body from origin after 4 s will be `21.5 m`.
Reason : The equation `v=u+a t` can be applied to obtain v if a is constant.

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of assertion.
B. If both Assertion and Reason are correct but Reason in not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the problem step by step, we will analyze the assertion and reason provided in the question.

### Step 1: Identify Given Information
- Mass of the body, \( m = 4 \, \text{kg} \)
- Initial velocity, \( \mathbf{u} = 5 \hat{i} \, \text{m/s} \)
- Force acting on the body, \( \mathbf{F} = 4 \hat{j} \, \text{N} \)
- Time, \( t = 4 \, \text{s} \)

### Step 2: Calculate Acceleration
Using Newton's second law, the acceleration \( \mathbf{a} \) can be calculated as:
\[ \mathbf{a} = \frac{\mathbf{F}}{m} \]
Substituting the values:
\[ \mathbf{a} = \frac{4 \hat{j}}{4} = 1 \hat{j} \, \text{m/s}^2 \]

### Step 3: Calculate Displacement
The formula for displacement \( \mathbf{s} \) when initial velocity, acceleration, and time are known is:
\[ \mathbf{s} = \mathbf{u} t + \frac{1}{2} \mathbf{a} t^2 \]
Substituting the known values:
\[ \mathbf{s} = (5 \hat{i}) (4) + \frac{1}{2} (1 \hat{j}) (4^2) \]
Calculating each term:
\[ \mathbf{s} = 20 \hat{i} + \frac{1}{2} (1 \hat{j}) (16) = 20 \hat{i} + 8 \hat{j} \]
Thus, the displacement vector is:
\[ \mathbf{s} = 20 \hat{i} + 8 \hat{j} \, \text{m} \]

### Step 4: Calculate Magnitude of Displacement
The magnitude of displacement \( s \) can be calculated using the Pythagorean theorem:
\[ s = \sqrt{(20)^2 + (8)^2} = \sqrt{400 + 64} = \sqrt{464} \approx 21.5 \, \text{m} \]

### Step 5: Conclusion on Assertion
The assertion states that the displacement of the body from the origin after 4 seconds will be \( 21.5 \, \text{m} \). From our calculations, this is indeed true.

### Step 6: Conclusion on Reason
The reason states that the equation \( v = u + at \) can be applied to obtain \( v \) if \( a \) is constant. This is also true, but it does not directly explain the assertion regarding displacement. Therefore, while both the assertion and reason are true, the reason does not correctly explain the assertion.

### Final Answer
- **Assertion**: True
- **Reason**: True, but not the correct explanation for the assertion.