94

Chapter 3Acceleration and Free Fall

Summary

Selected Vocabulary

gravity...............................A general term for the phenomenon of attraction between things having

mass. The attraction between our planet and a human-sized object causes

the object to fall.

acceleration.......................The rate of change of velocity; the slope of the tangent line on a v-t graph.

Notation

a........................................acceleration

g........................................the acceleration of objects in free fall

Summary

Galileo showed that when air resistance is negligible all falling bodies have the same motion regardless of

mass. Moreover, their v-t graphs are straight lines. We therefore define a quantity called acceleration as the

slope,

.

v/

.

t, of an object’s v-t graph. In cases other than free fall, the v-t graph may be curved, in which case

the definition is generalized as the slope of a tangent line on the v-t graph. The acceleration of objects in free

fall varies slightly across the surface of the earth, and greatly on other planets.

Positive and negative signs of acceleration are defined according to whether the v-t graph slopes up or

down. This definition has the advantage that a force in a given direction always produces the same sign of

acceleration.

The area under the v-t graph gives

.

x, and analogously the area under the a-t graph gives

.

v.

For motion with constant acceleration, the following three equations hold:

.

x=v

o

.

t+

1

2

a

.

t

2

v

f2

=v

o2

+2a

.

x

a=

.

v

.

t

They are not valid if the acceleration is changing.