Show here are the velocity and acceleration vectors for an object in several different types of motion. In which case is the object slowing down and turning to the left ?

Options

A.
B.
C.
D.

Answer

To determine in which case the object is slowing down and turning to the left, we need to analyze the relationship between the velocity and acceleration vectors in the given options. Here’s a step-by-step solution:

### Step 1: Understand the Concepts
- **Velocity Vector**: Indicates the direction in which the object is moving.
- **Acceleration Vector**: Indicates the change in velocity. If the acceleration is in the opposite direction to the velocity, the object is slowing down (deceleration).
- **Turning Left**: For an object to be turning left, the acceleration vector must have a component directed to the left.

### Step 2: Analyze Each Option
We have four options (A, B, C, D) to analyze.

#### Option A:
- **Velocity and Acceleration Direction**: Both vectors point in the same direction.
- **Conclusion**: The object is speeding up, not slowing down. **(Incorrect)**

#### Option B:
- **Velocity Direction**: The velocity vector points in one direction.
- **Acceleration Direction**: The acceleration vector points in the opposite direction to the velocity and has a leftward component.
- **Conclusion**: The object is slowing down and has a leftward component in acceleration. **(Correct)**

#### Option C:
- **Velocity and Acceleration Direction**: The vectors are perpendicular to each other.
- **Conclusion**: This represents uniform motion; the object is neither speeding up nor slowing down. **(Incorrect)**

#### Option D:
- **Velocity and Acceleration Direction**: Both vectors point in the same direction.
- **Conclusion**: The object is speeding up. **(Incorrect)**

### Step 3: Final Conclusion
After analyzing all options, we find that **Option B** is the correct answer as it satisfies both conditions: the object is slowing down and turning to the left.