Why does $d$ mean?

Question

I am told that force can be given as a rate of change of momentum:

$$F = \frac{p}{t} = \frac{dp}{dt}$$

What do the $d$'s mean? I've seen them in other formulas as well.

Answer 1

The d's mean "derivative of p with respect to t." This is standard calculus notation.

Answer 2

In the equation you have given $F = \frac{p}{t}$

But in general, the change in p with respect to t might not be constant, and thus the fraction must be represented by a derivative, which represents the rate of change of some quantity with respect to another one, in this case $\frac{dp}{dt}$ represents the rate of change of p with respect to a small change in t.