If an object is moved twice as far while the same force is applied, what happens to the work done?

When considering the relationship between force, distance, and work done, the formula for work is essential: Work is defined as the product of the force applied to an object and the distance over which that force is applied. In mathematical terms, this is expressed as:

[ \text{Work} = \text{Force} \times \text{Distance} ]

If an object is moved twice as far while applying the same force, you can represent the change in work done as follows. Let’s denote the original distance moved as ( d ). The work done on the object when it is moved this distance would be:

[ \text{Work}_{1} = \text{Force} \times d ]

Now, if the object is moved twice that distance ( (2d) ) while applying the same force, the new work done is:

[ \text{Work}_{2} = \text{Force} \times (2d) ]

This can be simplified to:

[ \text{Work}_{2} = 2 \times (\text{Force} \times d) ]

This equation clearly shows that the work done has now doubled compared to the initial work calculated. Hence, when the distance is increased