W = F × S ×(COS theeta)W = F × S × (COS 180degree)( since, angle formed will be 180)w = F×S × 1 ( since the value of cos180 degree is 1)hence,W = F×S will be the answer

Expression for the Work Done when a Force is Acting on an Object in the Direction of its Displacement

Definition of Work:
Work is defined as the transfer of energy that occurs when a force is applied to an object, causing it to move in the direction of the force.

Mathematical Expression for Work:
The mathematical expression for work is given by the formula:

Work (W) = Force (F) × Displacement (d) × cos(θ)

where:
- Work (W) is the amount of energy transferred or done on the object,
- Force (F) is the magnitude of the force applied on the object,
- Displacement (d) is the distance the object moves in the direction of the force,
- θ (theta) is the angle between the force vector and the displacement vector.

Explanation:
When a force is acting on an object and causing it to move in the direction of the force, work is being done on the object. Let's break down the components of the work formula to understand it better:

1. Force (F):
The force applied on the object determines the amount of work done. The greater the force, the more work is done on the object. The force can be applied in various ways, such as pushing, pulling, or gravity acting on the object.

2. Displacement (d):
The displacement is the distance the object moves in the direction of the force. It is important to note that only the displacement in the direction of the force contributes to the work done. If the object moves perpendicular to the force, the displacement in that direction does not contribute to the work done.

3. Angle between Force and Displacement (θ):
The angle between the force vector and the displacement vector is denoted by θ (theta). The cosine of this angle is multiplied with the force and displacement to calculate the work done. When the force and displacement are in the same direction (θ = 0), the cosine of 0 is 1, resulting in maximum work done. If the force and displacement are perpendicular (θ = 90°), the cosine of 90° is 0, resulting in no work done.

The work done can be positive, negative, or zero depending on the sign of the force and the angle between the force and displacement. If the force and displacement are in the same direction, the work done is positive. If they are in opposite directions, the work done is negative. If the force and displacement are perpendicular, the work done is zero.

Conclusion:
The expression for the work done when a force is acting on an object in the direction of its displacement is given by the formula: Work (W) = Force (F) × Displacement (d) × cos(θ). This formula allows us to calculate the amount of energy transferred or done on an object based on the force applied, the distance it moves, and the angle between the force and displacement vectors.