Explaining Projectile Motion Equation

Question

Hi! I'm doing a project where I have to use the projectile motion equation s = -16t² + v₀t + s₀. I'm trying to do a write up where I explain the different parts of this equation, and I understand what each variable means, but I don't understand why they are in the order they are in. For example, I understand what -16 and t represent, but I don't know why -16t² is included in the equation, nor do I understand why v₀ is multiplied by t, and I also don't understand why they are all added together in the way they are. If anyone would be so kind as to explain how this equation was developed I would be super grateful.

Answer 1

I think the easiest shortest solution is that you use a polynomial because it properly accounts for gravity and the motion of the ball, that is that there are two times it hits the same height, just that one had a positive velocity and the other time it has a negative one .

Because gravity is in the negative direction and your throw is in the positive direction, they will work against each other. That is until it hits a max height where velocity is zero and then the acceleration and velocity works with each other. This means a negative. The motion itself acts like a parabola so it only makes sense that the equation is going to be a parabola. An equation can mean something you visually see but put into mathematical syntax.