86
t
v
x
a
t
v
x
a
t
v
x
a
1
2
3
Discussion question B.
position
velocity
acceleration
slope of
tangent line
slope of
tangent line
curvature
=rate of change of position
=rate of change of velocity
0
5
10
0
1
2
3
4
0
1
012345
t (s)
10
20
30
40
200
400
600
0
5
02468101214
t (s)
0
0
(a)(b)
50
(c)
Chapter 3Acceleration and Free Fall
between v and x, we can also make graphs of acceleration as a function of
time, as shown in figures (a) and (b) above.
Figure (c) summarizes the relationships among the three types of
graphs.
Discussion questions
A. Describe in words how the changes in the a-t graph for the skydiver relate
to the behavior of the v-t graph.
B. Explain how each set of graphs contains inconsistencies.
C. In each case, pick a coordinate system and draw x-t, v-t, and a-t graphs.
Picking a coordinate system means picking where you want x=0 to be, and
also picking a direction for the positive x axis.
1. An ocean liner is crusing in a straight line at constant speed.
2. You drop a ball. Draw to different sets of graphs (a total of 6), with one
set's positive x axis pointing in the opposite direction compared to the
other's.
3. You're driving down the street looking for a house you've never been to
before. You realize you've passed the address, so you slow down, put the
car in reverse, back up, and stop in front of the house.