When the work done is positive:
1. Definition:
- Work is said to be positive when the force applied on an object is in the same direction as the displacement of the object.
- Mathematically, work done (W) is positive when the angle between the force vector and the displacement vector is less than 90 degrees.

2. Example:
- Pushing a car in the forward direction: When a person pushes a car, the force applied is in the same direction as the displacement of the car. As a result, the work done on the car is positive.

3. Explanation:
- In this scenario, the force and displacement vectors have the same direction, which means the angle between them is less than 90 degrees.
- Positive work indicates that energy is transferred to the object being acted upon.
- The object gains energy as a result of the work done on it.

4. Visual representation:
- [Image: Car being pushed forward with an arrow indicating the direction of the force and displacement]

When the work done is negative:
1. Definition:
- Work is said to be negative when the force applied on an object is in the opposite direction to the displacement of the object.
- Mathematically, work done (W) is negative when the angle between the force vector and the displacement vector is greater than 90 degrees.

2. Example:
- Pulling a suitcase in the opposite direction: When a person pulls a suitcase in the opposite direction of its motion, the force applied is opposite to the displacement of the suitcase. As a result, the work done on the suitcase is negative.

3. Explanation:
- In this scenario, the force and displacement vectors have opposite directions, which means the angle between them is greater than 90 degrees.
- Negative work indicates that energy is transferred away from the object being acted upon.
- The object loses energy as a result of the work done on it.

4. Visual representation:
- [Image: Suitcase being pulled backward with an arrow indicating the direction of the force and displacement]

Conclusion:
- Work done can be positive or negative depending on the relative directions of the force and displacement vectors.
- Positive work occurs when the force and displacement vectors have the same direction, while negative work occurs when they have opposite directions.
- Positive work transfers energy to the object, while negative work transfers energy away from the object.
- Understanding the sign of work done helps in analyzing the energy transfer and the effect on the object being acted upon.