<Tr> <Td> Instantaneous velocity v i (\ displaystyle \ v_ (i) \) of a falling object that has travelled distance d (\ displaystyle \ d \) on a planet with mass M (\ displaystyle \ M \), with the combined radius of the planet and altitude of the falling object being r (\ displaystyle \ r \), this equation is used for larger radii where g (\ displaystyle \ g \) is smaller than standard g (\ displaystyle \ g \) at the surface of Earth, but assumes a small distance of fall, so the change in g (\ displaystyle \ g \) is small and relatively constant: </Td> <Td> v i = 2 G M d r 2 (\ displaystyle \ v_ (i) = (\ sqrt (\ frac (2GMd) (r ^ (2)))) \) </Td> </Tr> <Tr> <Td> Instantaneous velocity v i (\ displaystyle \ v_ (i) \) of a falling object that has travelled distance d (\ displaystyle \ d \) on a planet with mass M (\ displaystyle \ M \) and radius r (\ displaystyle \ r \) (used for large fall distances where g (\ displaystyle \ g \) can change significantly): </Td> <Td> v i = 2 G M (1 r − 1 r + d) (\ displaystyle \ v_ (i) = (\ sqrt (2GM (\ Big () (\ frac (1) (r)) - (\ frac (1) (r + d)) (\ Big)))) \) </Td> </Tr> <P> The first equation shows that, after one second, an object will have fallen a distance of 1 / 2 × 9.8 × 1 = 4.9 meters . After two seconds it will have fallen 1 / 2 × 9.8 × 2 = 19.6 meters; and so on . The second to last equation becomes grossly inaccurate at great distances . If an object fell 10,000 meters to Earth, then the results of both equations differ by only 0.08%; however, if it fell from geosynchronous orbit, which is 42,164 km, then the difference changes to almost 64% . </P> <P> Based on wind resistance, for example, the terminal velocity of a skydiver in a belly - to - earth (i.e., face down) free - fall position is about 195 km / h (122 mph or 54 m / s). This velocity is the asymptotic limiting value of the acceleration process, because the effective forces on the body balance each other more and more closely as the terminal velocity is approached . In this example, a speed of 50% of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on . </P>

How far do you fall in two seconds