Newton's laws in X2? (1 Viewer)

[00iCon]

I was exploring the syllabus and found this:"use Newton’s laws to obtain equations of motion of a particle in situationsother than projectile motion and simple harmonic motion"how do Newton's laws relate to integration and differentiation?

 

[mitchy_boy]

Because Newton gave birth to maths.

 

[00iCon]

I should've read a little further "The classical statement of Newton’s First and Second laws of motion should be given as an illustration of the application of calculus to the physical world. Resolution of forces, accelerations and velocities in horizontal and vertical directions is to be used to obtain the appropriate equations of motion in two dimensions."
Question: Would the other motions from my first post be just linear motion?

 

[jet]

Yeah. But you also use the Third Law when you resolve forces. So, it's basically all the types of motion; circular, resisted, banked tracks etc.

 

[- Alex -]

Newton invented Calculus, that why.

 

[jet]

Newton invented Calculus, that why.

It wasn't just him; Leibniz is also credited with the introductory formulation of Calculus, but the idea of infinitesimals existed long before that.

Basically, using newton's laws you gain an equation for acceleration in terms of position, velocity or time (or even a combination of them). Since acceleration is the derivative of velocity, and velocity the derivative of displacement(position), then integrating will give you the equations of motion.