A body lying initially at point (3,7) starts moving with a constant acceleration of `4 hati`. Its position after 3s is given by the coordinates

Options

A. (7,3)
B. (7,18)
C. (21,7)
D. (3,7)

Explanation

To find the position of a body after 3 seconds given its initial position and constant acceleration, we can follow these steps:

### Step 1: Identify the initial conditions
The body is initially at point (3, 7), which can be represented as a position vector:
\[ \mathbf{r}_0 = 3 \hat{i} + 7 \hat{j} \]
The initial velocity (\( \mathbf{u} \)) is zero since the body starts from rest:
\[ \mathbf{u} = 0 \]

### Step 2: Determine the acceleration
The body has a constant acceleration of \( 4 \hat{i} \):
\[ \mathbf{a} = 4 \hat{i} \]

### Step 3: Use the kinematic equation to find the displacement
We can use the kinematic equation for displacement:
\[ \mathbf{s} = \mathbf{u} t + \frac{1}{2} \mathbf{a} t^2 \]
Substituting the known values:
- \( \mathbf{u} = 0 \)
- \( t = 3 \) seconds
- \( \mathbf{a} = 4 \hat{i} \)

The equation simplifies to:
\[ \mathbf{s} = 0 + \frac{1}{2} (4 \hat{i}) (3^2) \]
Calculating \( t^2 \):
\[ 3^2 = 9 \]
Now substituting this back:
\[ \mathbf{s} = \frac{1}{2} (4 \hat{i}) (9) = 2 \cdot 4 \cdot 9 \hat{i} = 18 \hat{i} \]

### Step 4: Calculate the final position vector
Now, we can find the final position vector \( \mathbf{r} \) after 3 seconds:
\[ \mathbf{r} = \mathbf{r}_0 + \mathbf{s} \]
Substituting the values:
\[ \mathbf{r} = (3 \hat{i} + 7 \hat{j}) + (18 \hat{i}) = (3 + 18) \hat{i} + 7 \hat{j} = 21 \hat{i} + 7 \hat{j} \]

### Step 5: Write the final coordinates
The final coordinates of the body after 3 seconds are:
\[ (21, 7) \]

### Conclusion
Thus, the position of the body after 3 seconds is \( (21, 7) \).

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