Question

What does the slope of an force vs. displacement time represent?

I know that the area under the graph represents work, but what does the slope represent?

Answer 1

Literally the slope means force per unit distance or force gradient. An example is spring constant.

Explanation:

The spring constant is `k= F/(Deltax)`
F is force applied to stretch a spring and causes it to extend by a length `Deltax` from its neutral position. If the neutral position is 0, then the displacement `Deltax = x-0= x`

Let's say `k = 50 N/m`. It means that 50 N is required for every meter being stretched. If you graph `F` v `Deltax`, you get the slope `k`. Therefore the slope of the spring force F vs. x is the spring constant.