I got a lot done this week. I had initially set the goals of reviewing the Algebra 2 material I’d forgotten and adding in a horizontal element to the Projectile Motion Equation. In addition, I had set a stretch goal of beginning the process of learning acceleration curves. To my pleasant surprise, these goals turned out to be significantly easier than I had anticipated. So much easier in fact, that I was able to complete them and begin the next step, adding a Jerk Term to my equation. (Yes, that is actually the technical term used.)
I started out simple, and plan to slowly add to my equation until it’s completed. First, I assumed you had a rocket, at a given height. Simple enough, f(t) = h, with f(t) being your height at a given t, which is time. Next, I let my rocket move, adding a Velocity Term. f(t) = Vt + h, now instead of a horizontal line we have a linear equation, we’re moving up in the world. Next I added an acceleration term. f(t) = ½at^2 + Vt + h. You need to half the acceleration term because you need to average it with 0. You need to use time squared because acceleration is distance over time squared, so you need to multiply by time squared to get a distance. In addition, this acceleration term is when you can start to incorporate gravity into your equation, as gravity is a force of acceleration. During this process, I had to ask my dad to teach me trigonometry. This was so that if I was given an acceleration at an angle (for example, if I were launching at an angle) I could calculate the horizontal and vertical elements of the acceleration. This is done using the sine and cosine functions. Finally, once I felt I had a firm grasp on acceleration curves, I moved on to jerk curves (Jerk is your change in acceleration over time), however I’ve not yet made much progress on the subject. Attached below is a picture of my Acceleration Curve Notes.
