section_path: Laws/Examples/Uniformly accelerated motion
section_name: Uniformly accelerated motion
paragraph_text: Uniformly accelerated motion
  
  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. 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 law of universal gravitation. The latter states that the magnitude of the gravitational force from the Earth upon the body is F = G M m r 2, {\displaystyle F={\frac {GMm}{r^{2}}},} where m {\displaystyle m} is the mass of the falling body, M {\displaystyle M} is the mass of the Earth, G {\displaystyle G} is Newton's constant, and r {\displaystyle r} 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 m a {\displaystyle ma}, the body's mass m {\displaystyle m} cancels from both sides of the equation, leaving an acceleration that depends upon G {\displaystyle G}, M {\displaystyle M}, and r {\displaystyle r}, and r {\displaystyle r} can be taken to be constant. This particular value of acceleration is typically denoted g {\displaystyle g}: g = G M r 2 ≈ 9.8 m / s 2. {\displaystyle g={\frac {GM}{r^{2}}}\approx \mathrm {9.8~m/s^{2}}.}
  
  If the body is not released from rest but instead launched upwards and/or horizontally with nonzero velocity, then free fall becomes projectile motion. 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 g {\displaystyle g} downwards, as it is at all times. Setting the wrong vector equal to zero is a common confusion among physics students.