# Kinematics of a body in movement with air drag

Let's assume i got this body (red one) wich is moving along the x-axis. It has got two forces on it, one called $F$, which is constant, and the other called $D$ which is the drag caused by the air that will vary. Could i describe its movement with these equations and using small intervals of time, for example: $t=0.001\ \rm s$ Getting the acceleration with Newton's Second Law where $F$ is constant and $D$, which is drag, will vary depending the velocity.

$$A=\frac{(F-D)}{m}$$

Equation to calculate drag. Here i assume $\rho$, $Cd$, and $A$ to be constant. $$D=0.5\rho* Cd * A *v^2$$ Equation to calculate velocity. $$v=v_o+at$$

Equation to calculate position. $$x=x_0+v_0t+0.5at^2$$

Assuming everything said let's go for and example. We have that: $$F=100\ \rm N$$ $$v_0=0 \ \rm m/s$$

I first calculate the $a$ (acceleration) assuming that $D$ is $0$ beacuse $v_0 = 0\ \rm m/s$. When we got $a$ we use it with the velocity equation to get the velocity. Then we use all the variables in the position equation to get the position. Then, with the velocity we have calcualted we get the drag force and then we get a different acceleration which i will use to calculate another time the $v$ and $x$, and the i would continue doing the same thing with these intervals of $t=0.001\ \rm s$. I have computed that and i finally get a constant velocity, which i supose it is the "terminal velocity".

Can this be done this way?

• Hi, welcome to Physics SE! Please don't post formulae as pictures or plain text, but use MathJax instead. MathJax is easy for people on all devices to read, and can show up clearer on different screen sizes and resolutions. I've edited it here as an example. Look at this Math SE meta post for a quick tutorial. – user191954 Aug 19 '18 at 16:24
• You might start here with no drag feynmanlectures.caltech.edu/I_09.html and then this paper physics.bu.edu/py502/lectures3/cmotion.pdf – Farcher Aug 19 '18 at 17:59
• @Chair I have been using another page, however, i will take a look on it. Thanks! – DeFabregas Aug 19 '18 at 19:50
• @Farcher They seem interesting, i will have a look. Thanks! – DeFabregas Aug 19 '18 at 19:50

## 1 Answer

Yes.You are going right .

Now you just need to form differential equation and solve it. You can make differential equation in terms of $v$, this way it will be of first order and you can easily solve it.

• you use A for acceleration and A for area? – Eli Aug 19 '18 at 16:32
• @Eli It was an error, i use A for area and a for acceleration. – DeFabregas Aug 19 '18 at 19:51