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Chapter 2: 1D Kinematics - Lesson 5: Free Fall and the Acceleration of Gravity

How Fast? and How Far?

  1. Introduction
  2. Acceleration of Gravity
  3. Representing Free Fall by Graphs
  4. How Fast? and How Far?
  5. The Big Misconception
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Hold down the T key for 3 seconds to activate the audio accessibility mode, at which point you can click the K key to pause and resume audio. Useful for the Check Your Understanding and See Answers.

Free-falling objects are in a state of acceleration. Specifically, they are accelerating at a rate of 9.8 m/s/s. This is to say that the velocity of a free-falling object is changing by 9.8 m/s every second. If dropped from a position of rest, the object will be traveling 9.8 m/s (approximately 10 m/s) at the end of the first second, 19.6 m/s (approximately 20 m/s) at the end of the second second, 29.4 m/s (approximately 30 m/s) at the end of the third second, etc. Thus, the velocity of a free-falling object that has been dropped from a position of rest is dependent upon the time that it has fallen. The formula for determining the velocity of a falling object after a time of t seconds is

vf = g * t

(dropped from rest)
 

where g is the acceleration of gravity. The value for g on Earth is 9.8 m/s/s. The above equation can be used to calculate the velocity of the object after any given amount of time when dropped from rest. Example calculations for the velocity of a free-falling object after six and eight seconds are shown below.

Example Calculations:

At t = 6 s
vf = (9.8 m/s2) * (6 s) = 58.8 m/s

At t = 8 s
vf = (9.8 m/s2) * (8 s) = 78.4 m/s

The distance that a free-falling object has fallen from a position of rest is also dependent upon the time of fall. This distance can be computed by use of a formula; the distance fallen after a time of t seconds is given by the formula.

d = 0.5 * g * t2

(dropped from rest)
 

where g is the acceleration of gravity (9.8 m/s/s on Earth). Example calculations for the distance fallen by a free-falling object after one and two seconds are shown below.

 



 

Example Calculations:

At t = 1 s
d = (0.5) * (9.8 m/s2) * (1 s)2 = 4.9 m

At t = 2 s
d = (0.5) * (9.8 m/s2) * (2 s)2 = 19.6 m

At t = 5 s
d = (0.5) * (9.8 m/s2) * (5 s)2 = 123 m
(rounded from 122.5 m)

The diagram below (not drawn to scale) shows the results of several distance calculations for a free-falling object dropped from a position of rest.







 
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