A car is moving in east direction. It takes a right turn and moves along south direction without change in its speed. What is the direction of average acceleration of the car?

Options

A. North east
B. South east
C. North west
D. South west

Explanation

To find the direction of the average acceleration of the car as it makes a right turn from moving east to moving south, we can follow these steps:

### Step 1: Identify the Initial and Final Velocities
- The car is initially moving in the east direction. We can denote this initial velocity vector as \( \vec{v_i} \).
- After taking a right turn, the car moves in the south direction. We can denote this final velocity vector as \( \vec{v_f} \).

### Step 2: Represent the Velocity Vectors
- Let's represent the initial velocity \( \vec{v_i} \) as a vector pointing to the right (east).
- The final velocity \( \vec{v_f} \) will be represented as a vector pointing downward (south).

### Step 3: Calculate the Change in Velocity
- The change in velocity \( \Delta \vec{v} \) can be calculated using the formula:
\[ \Delta \vec{v} = \vec{v_f} - \vec{v_i} \]
- Since \( \vec{v_f} \) is pointing south and \( \vec{v_i} \) is pointing east, we can express this as:
\[ \Delta \vec{v} = \vec{v_f} + (-\vec{v_i}) \]
- Here, \( -\vec{v_i} \) is the vector pointing west (the opposite direction of east).

### Step 4: Visualize the Vectors
- Now, we can visualize the vectors:
- \( \vec{v_i} \) points east.
- \( -\vec{v_i} \) points west.
- \( \vec{v_f} \) points south.
- To find the resultant vector \( \Delta \vec{v} \), we can use the vector addition of \( \vec{v_f} \) and \( -\vec{v_i} \).

### Step 5: Use the Parallelogram Law
- According to the parallelogram law of vector addition, we can represent the two vectors (south and west) as adjacent sides of a parallelogram.
- The diagonal of this parallelogram will give us the direction of the change in velocity \( \Delta \vec{v} \).

### Step 6: Determine the Direction of Average Acceleration
- The average acceleration \( \vec{a_{avg}} \) is given by:
\[ \vec{a_{avg}} = \frac{\Delta \vec{v}}{\Delta t} \]
- Since \( \Delta \vec{v} \) points in the direction of the diagonal of the parallelogram formed by the south and west vectors, the direction of the average acceleration will be in the southwest direction.

### Conclusion
Thus, the direction of the average acceleration of the car after it takes a right turn and moves south is **southwest**.