# Velocity & Acceleration

[Chapter 2 Objectives]

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## Free Fall Acceleration

About 1600, Galileo performed his famous inclined plane experiments and discovered that the acceleration of a freely-falling object is constant - that is, the object's acceleration does not change while the object is in free fall. The acceleration of a freely-falling object - any freely-falling object - near the surface of the Earth is about 9.8 m/s2 (which is conveniently close to 10 m/s2 for rough calculations). In the "customary" system of units, g = 32 ft/s2 or about 22 mi/hr/s. This acceleration value is commonly called "g". The direction of this acceleration is downward (toward the center of the Earth).

Free fall acceleration is different on other planets - it depends on the planet's size and mass. The table below shows some approximate values of "g" for selected objects in our solar system.

Acceleration of gravity, "g" in the Solar System

At the surface of

g (m/s2) is

Mass (kg)*

Sun1

275
1.99 x 1030
6.95 x 108

Mercury

3.7
3.30 x 1023
2.44 x 106

Venus

8.9
4.87 x 1924
6.05 x 106

Earth

9.8
5.97 x 1024
6.38 x 106

Moon (of Earth)

1.6
7.35 x 1022
1.73 x 106

Mars

3.7
6.42 x 1023
3.40 x 106

Phobos (moon of Mars)

6.0 x 10-3
1.08 x 1016
1.1 x 104

Deimos (moon of Mars)

3.3 x 10-3
1.80 x 1015
6 x 103

Jupiter1

25
1.90 x 1027
7.15 x 107

Ganymede (moon of Jupiter)

1.4
1.48 x 1023
2.63 x 106

Europa (moon of Jupiter)

1.3
4.80 x 1022
1.57 x 106

Saturn1

10.4
5.68 x 1026
6.03 x 107

Uranus1

8.9
8.68 x 1025
2.56 x 107

Neptune1

11
1.02 x 1026
2.48 x 107

Pluto

0.7

1.27 x 1022

1.14 x 106
1Assuming that these objects actually had a surface...

*Mass and radius data taken from The Nine Planets

## Free Fall Velocity

To say that the acceleration of a freely-falling object is constant means that the velocity of a freely-falling object changes at a constant rate.

If we say that g = 10 m/s2, therefore, we mean that the velocity of the falling object changes by 10 m/s each second that it falls. If we drop it from rest, it will be going 10 m/s downward in 1 second, 20 m/s downward in 2 seconds, 30 m/s in 3 seconds, and so on. As the object falls, its velocity increases by about 10 m/s each second. In tabular form:

time (s)

velocity (m/s)

0
0
1
10
2
20
3
30
4
40
5
50
6
60
7
70

Since free fall is a motion with constant acceleration, the kinematics equations for constant acceleration apply. Particularly, the equations:

and

can be used to calculate an object's velocity in free fall.

[Chapter 2 Objectives]

BHS -> Staff -> Mr. Stanbrough -> Physics -> Mechanics -> Kinematics -> this page

last update July 28, 2001 by JL Stanbrough