Editing Newton's laws of motion (section)

====Uniformly accelerated motion====
{{Main|Free fall|Projectile motion}}
[[Image:Bouncing ball strobe edit.jpg|thumb|upright=1.3|A [[bouncing ball]] photographed at 25 frames per second using a [[stroboscope|stroboscopic flash]]. In between bounces, the ball's height as a function of time is close to being a [[parabola]], deviating from a parabolic arc because of air resistance, spin, and deformation into a non-spherical shape upon impact.]]
If a body falls from rest near the surface of the Earth, then in the absence of air resistance, it will accelerate at a constant rate. This is known as [[free fall]]. The speed attained during free fall is proportional to the elapsed time, and the distance traveled is proportional to the square of the elapsed time.<ref>{{Cite journal |last=Nicodemi |first=Olympia |author-link=Olympia Nicodemi |date=2010-02-01 |title=Galileo and Oresme: Who Is Modern? Who Is Medieval? |url=https://doi.org/10.4169/002557010X479965 |journal=[[Mathematics Magazine]] |volume=83 |issue=1 |pages=24–32 |doi=10.4169/002557010X479965 |s2cid=122113958 |issn=0025-570X}}</ref> Importantly, the acceleration is the same for all bodies, independently of their mass. This follows from combining Newton's second law of motion with his [[Newton's law of universal gravitation|law of universal gravitation]]. The latter states that the magnitude of the gravitational force from the Earth upon the body is
<math display="block">F = \frac{GMm}{r^2} ,</math>
where <math>m</math> is the mass of the falling body, <math>M</math> is the mass of the Earth, <math>G</math> is Newton's constant, and <math>r</math> is the distance from the center of the Earth to the body's location, which is very nearly the radius of the Earth. Setting this equal to <math>ma</math>, the body's mass <math>m</math> cancels from both sides of the equation, leaving an acceleration that depends upon <math>G</math>, <math>M</math>, and <math>r</math>, and <math>r</math> can be taken to be constant. This particular value of acceleration is typically denoted <math>g</math>:
<math display="block">g = \frac{GM}{r^2} \approx \mathrm{9.8 ~m/s^2}.</math>

If the body is not released from rest but instead launched upwards and/or horizontally with nonzero velocity, then free fall becomes [[projectile motion]].<ref>{{cite web|url=https://webhome.phy.duke.edu/~schol/phy361/faqs/faq3/ |first=Kate |last=Scholberg |author-link=Kate Scholberg |access-date=2022-01-16 |title=Frequently Asked Questions: Projectile Motion |website=Physics 361 |year=2020}}</ref> When air resistance can be neglected, projectiles follow [[parabola]]-shaped trajectories, because gravity affects the body's vertical motion and not its horizontal. At the peak of the projectile's trajectory, its vertical velocity is zero, but its acceleration is <math>g</math> downwards, as it is at all times. Setting the wrong vector equal to zero is a common confusion among physics students.<ref>{{Cite journal |last1=Carli |first1=Marta |last2=Lippiello |first2=Stefania |last3=Pantano |first3=Ornella |last4=Perona |first4=Mario |last5=Tormen |first5=Giuseppe |date=2020-03-19 |title=Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context |journal=[[Physical Review Physics Education Research]] |language=en |volume=16 |issue=1 |pages=010111 |doi=10.1103/PhysRevPhysEducRes.16.010111 |bibcode=2020PRPER..16a0111C |s2cid=215832738 |issn=2469-9896|doi-access=free |hdl=11577/3340932 |hdl-access=free }}</ref>