The difference in using Distance vs Displacement is demonstrated in this example:
Work = Force x Distance
If I carry an object to and fro 10 metres, the work done would be Force x 20 metres.
and
Work = Force x Displacement
If I carry an object to and fro 10 metres, the work done would be
Force x 0 metres.
In this context, which should be a more accurate representation or formula? I note that Force and displacement are vectors and distance as scalar.
Best Answer
It depends on whether the force field is conservative or not.
Example of a conservative force is gravity. Lifting, then lowering an object against gravity results in zero net work against gravity.
Friction is non-conservative: the force is always in the direction opposite to the motion. Moving 10 m one way, you do work. Moving back 10 m, you do more work.
As @lemon pointed out in a comment, this is expressed by writing the work done as the integral:
$$W = \int \vec F \cdot d\vec{x}$$
When $F$ is only a function of position and $\vec \nabla\times \vec F = 0$, this integral is independent of the path and depends only on the end points; but if it is a function of direction of motion, you can no longer do the integral without taking the path into account.