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Explanation of Gravity Equations for Falling Objects - Succeed in Physical Science. Also refer to physics, force, mass, gravitational constant, acceleration, velocity, distance, time, calculation, square, square-root, Ron Kurtus, School for Champions. Copyright © Restrictions Gravity Equations for Falling Objectsby Ron Kurtus (23 August 2007) There are simple equations for falling objects that allow you to calculate the velocity and distance traveled, as well as the time taken to achieve a given velocity or distance. These equations are based on the fact that the force of gravity for objects relatively close to Earth equals the mass of the object times the acceleration due to gravity (F = mg). The acceleration due to gravity (g) is constant for all objects up to altitudes beyond many space satellites. From this simple equation, it is determined that the velocity, distance and time are independent of the mass of the object, provided air resistance is negligible. You normally do not need to memorize these equations, but you should know where to find them in order to solve equations. Questions you may have include:
This lesson will answer those questions. There is a mini-quiz near the end of the lesson. Useful tools: Metric-English Conversion | Scientific Calculator. VelocityIf you drop an object from some height, it will fall with increasing velocity. (We use velocity instead of speed, since the object is moving in a specific direction: down.) You can determine the object's velocity according to the time it has fallen by the equation: v = gt where
Note that the assumption is that air resistance on the object is negligible. An object that is lightweight or not heavy will probably be affected by air resistance. ExampleThus, if you drop an object from a tall building, its velocity after 4 seconds, it will be:
Distance in fallYou can find the distance traveled for a given time and to reach a velocity. Distance for a given timeUsing Calculus, you can derive the equation for the distance that the object falls in a given time. This equation is x = gt²/2 where
ExampleThe distance in meters that an object will fall in 3 seconds is:
Reaching given velocityBy substituting t = v/g and v = gt in the x = gt²/2 equation, you can get the distance traveled to reach a given velocity: x = v²/2g ExampleFor example, to find the distance required to reach 100 miles per hour (mph), you convert 100 mph to 146.7 feet/second. Thus:
That means you need to go up to over 336 feet to have a ball that you drop reach 100 mph. That is about the height of a 34-story building. Time to reach valueYou can find the time it takes to reach a given velocity or distance. Time to reach velocityTo determine the time it takes to reach a given velocity, you can rearrange v = gt into: t = v/g ExampleThus, the time it takes a falling object to reach a velocity of 49 m/s is t = (49 m/s) / (9.8 m/s²) = 5 seconds. Time to fall distanceTo determine the time it takes to fall a given distance, you can rearrange the equation x = gt²/2 into: t = SQRT(2x/g) where SQRT and √ mean the square root of the quantity in the parentheses (2x/g).
ExampleIf you dropped a weight from a height of 64 feet, you could calculate how long it takes to hit the ground.
Substituting t = 2 seconds into v = gt, you get a velocity of 64 feet/second. SummarySimple equations for falling objects allow you to calculate the velocity and distance traveled, as well as the time taken to achieve a given velocity or distance. These equations are based on force of gravity equation and the fact that the acceleration due to gravity (g) is constant for all objects up to altitudes beyond many space satellites. The equations are: v = gt, x = gt²/2, x = v²/2g, t = v/g and t = SQRT(2x/g). Typically, you don't need to memorize them but know where to find them in order to solve problems. Check your numbers ResourcesThe following resources provide information on this subject: WebsitesAcceleration of Gravity Calculations - from Western Washington University Books
Top-rated books on Simple Gravity Science
Top-rated books on Advanced Gravity Physics MiscellaneousMini-quiz to check your understanding1. What is the velocity in meters/second of an object that has been falling for 10 seconds? 2. How far in meters can an object fall in 10 seconds? 3. How long does it take an object weighing 100 pounds to fall 144 feet? If you got all three correct, you are on your way to becoming a Champion in Physical Science. If you had problems, you had better look over the material again. What do you think?Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. We will try to get back to you as soon as possible. Share linkFeel free to establish a link from your website to pages in this site. Or use our form to send this link to yourself or a friend. Students and researchersThe Web address of this page is Please include it as a reference in your report, document, or thesis. Where can you go from here?
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