Position function and its derivatives

In summary, the conversation discusses the origins of the position function and its relationship to velocity and acceleration. The speaker is curious about whether Newton created the function with the intention of deriving these concepts from it, or if it was discovered later on. They also mention the evolution of mathematics since Newton's time and the beauty of the subject.
  • #1
PapalPhysicist
5
0
Okay so I'm currently in cal 3. I've also taken physics 1 and 2. When I first saw the position function differentiated into velocity and then to acceleration I was awestruck. Math is beautiful and divinely structured. That's what I thought.

But as I've gone on and worked with it more and more a question has occurred. Newton created the basics of calculus. Much of what I have learned has been additions to his foundation, all the theorems and methods that allow for more complex integration and differentiation.

Now to my question. Did Newton create the position function? Was it created with the ability to then derive velocity and acceleration from it in mind?

Or was it something "discovered"?

I may be asking the wrong question here. Please guide me in the right direction if I am. The more math I've studied the more I see its beauty. I may not be the most studious but I'm definitely a curious person.
 
Physics news on Phys.org
  • #2
Mathematics was primitive when Newton was alive. Newton expressed his thinking more in sentences and diagrams than in functions and equations. A lot of the abstraction and symbology we use today in mathematics was developed since then.
 

Related to Position function and its derivatives

What is a position function?

A position function, also known as a displacement function, is a mathematical function that describes the position of an object over time. It takes into account the initial position, velocity, and acceleration of the object.

What are the derivatives of a position function?

The first derivative of a position function is velocity, which describes the rate of change of position. The second derivative is acceleration, which describes the rate of change of velocity.

How do I find the derivative of a position function?

To find the derivative of a position function, you can use the power rule, product rule, quotient rule, or chain rule depending on the form of the function. It is also important to keep track of the independent variable and use proper notation, such as d/dt for a function of time.

What is the relationship between position, velocity, and acceleration?

Position, velocity, and acceleration are all related through derivatives. Given a position function, the first derivative is velocity and the second derivative is acceleration. This means that the position function is the antiderivative of acceleration, and velocity is the antiderivative of position.

How are position functions used in real-world applications?

Position functions and their derivatives are used in various fields such as physics, engineering, and economics to analyze the motion and behavior of objects. They can also be used to predict future positions and make decisions based on the rate of change of position.

Similar threads

Force as a function of position, given x(t)
    • Mechanics
Replies
8
Views
4K
Classical Understanding Derivative of Position Function: Is Velocity Wrong?
    • Science and Math Textbooks
Replies
2
Views
810
B Speed/velocity as a derivative
    • Mechanics
Replies
6
Views
1K
Position and speed are enough in a physical system?
    • Mechanics
Replies
4
Views
906
I Finding Max and Min Extremes of a Function with Second Derivatives Equal to Zero
    • Differential Equations
Replies
1
Views
1K
Can the kinetic energy be a function of the position vector?
    • Mechanics
Replies
8
Views
3K
I [Questions] Modeling a Baseball Pitch Trajectory in 3D Space
    • Mechanics
Replies
1
Views
845
Is Impulse the anti derivative of momentum?
    • Mechanics
Replies
1
Views
6K
Understanding how time derivative = acceleration
    • General Discussion
Replies
12
Views
1K
Weirdness with this relative velocity formula when defining coordinate systems differently
    • Mechanics
Replies
26
Views
2K

Hot Threads

Recent Insights

Back
Top