What does $d$ stand for in this formula?

Question

Context: I am building a tennis ball machine and am having trouble interpreting the following formula for the flight path of the ball. I know all of the other values in the formula but the source I am using doesn't explicitly state what d is. I think it may be either distance or delta, any ideas?

If it helps the other variables are:
m = mass
t = time
Cd = drag coefficient
P = air density
g = gravity acceleration
Vx,y,z = components of translational velocity
Wx, Wy, Wz, = components of rotational speeds
C1 = life force coefficient
Thanks for the help!

Ryder Rude · Accepted Answer

Are you talking about things like $frac{d}{dt}$? $frac{dx}{dt}$ is meant to be interpreted as $frac{d}{dt}$ of $x$. $x$ is a function on which, when $frac{d}{dt}$ is applied, it gives another function. The two functions are related in the sense that the function $frac{dx}{dt}$ represents the rate at which the function $x$ changes as time passes. If $x$ is distance, then $frac{dx}{dt}$ is speed. Look up derivates. $d$ is not a variable, it's part of the notation for a derivative.

Correct answer by Ryder Rude on December 13, 2020

Dr jh · Answer

"d" stands for derivative. It's close to what you refer to as "delta" above ie., $Delta$ as in $frac{Delta x}{Delta t}$, but in the limit as these quantities become infinitesimally small. If you drew a graph of $x$ versus $t$, then the quantity $frac{Delta x}{Delta t}$ will be the gradient. Now think about wanting to know what the gradient is at any instant in time. This is what $frac{d x}{d t}$ is. The instantaneous gradient.
In the equations you mention above, $frac{d x}{d t}$ would represent the objects instantaneous velocity $v$, and $frac{d^2 x}{d t^2} = frac{d v}{d t} = a$ is the objects acceleration.

What does $d$ stand for in this formula?

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