Question

The velocity is given as \( \mathbf{v} = 3\hat{i} + 3\hat{j} \). Find the acceleration \( \mathbf{a} \).

• A. \( \mathbf{a} = 3\hat{i} + 3\hat{j} \)
• B. \( \mathbf{a} = 0 \)
• C. \( \mathbf{a} = 6\hat{i} + 6\hat{j} \)
• D. \( \mathbf{a} = 3\hat{i} + 6\hat{j} \)

Hint:

If the velocity vector is constant (does not change with time), the acceleration is zero.

Answer 1

The Correct Option is B

We are given that the velocity \( \mathbf{v} = 3\hat{i} + 3\hat{j} \). To find the acceleration \( \mathbf{a} \), we need to differentiate the velocity vector with respect to time.

1. Step 1: Understand the relationship between velocity and acceleration The acceleration is the rate of change of velocity with respect to time: \[ \mathbf{a} = \frac{d\mathbf{v}}{dt} \]

2. Step 2: Analyze the velocity The given velocity vector \( \mathbf{v} = 3\hat{i} + 3\hat{j} \) is a constant vector. This means that both the i-component (3) and the j-component (3) do not change over time.

3. Step 3: Differentiate the velocity Since the velocity vector is constant, its derivative with respect to time is zero: \[ \mathbf{a} = \frac{d}{dt}(3\hat{i} + 3\hat{j}) = 0 \] Therefore, the acceleration \( \mathbf{a} \) is zero.