XVA  Constant Velocity 1
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We are looking at the motion of an
object which is traveling at a constant velocity. This is the
first of two main pages that deal with constant velocity
graphs.
We are mostly concerned with the
relationship between the x vs. t graph and the v vs. t graph.
Each set of graphs will have a different value for
the constant velocity. Therefore, all of the accelerations
on this page are zero, or 0.0 m/s^{2}. So, all
of the a vs. t graphs appear the same. We are not much
concerned here with the a vs. t graphs. Our discussion
will center around the relationship between the x vs. t and
the v vs. t graphs.
[1] Here is the first of our constant
velocity examples. The object starts at the origin of its
position number line. The object's velocity is 0.0 m/s to
start with, and it remains at this value. So, the object
does not move. Since its velocity does not change, the
acceleration is 0.0 m/s^{2} throughout the motion.
Parameters: 
x_{o}
= 0.0 m 
v_{o}
= 0.0 m/s^{ } 
a =
0.0 m/s^{2 } 



The object's position
starts at 0.0 m, and it stays at that
location as time passes. 
The object's velocity
starts at 0.0 m/s. It's velocity remains
at that value as time passes. 
The constant acceleration
is 0.0 m/s^{2}; so, the velocity
does not change as time passes. 

[1] XVA demonstration 
Comments:
 The object is standing still. This
first set of graphs looks just like the first set in
the
constant position section. Here, however, the emphasis is on noting
that the velocity remains constant at a value of 0.0
m/s. This, of course, causes the object to remain
stationary.
 In all three of the above graphs the
graph line of the function is drawn directly over the
time axis. It may at first be difficult to see that there is
actually data shown on
these graphs.
 See
Constant
Velocity Animate 1.
[2]The object starts at the origin of its position number line.
At the start the object's velocity is 2.0 m/s, and it remains
at this value. So, the object moves away from the origin at
a constant speed in a positive direction. Since the velocity
of the object does not change, its acceleration is 0.0 m/s^{2}
throughout the motion.
Back
Parameters: 
x_{o}
= 0.0 m 
v_{o}
= 2.0 m/s^{ } 
a =
0.0 m/s^{2 } 



The object's position
starts at 0.0 m. It moves away from the
origin in a positive direction constantly
covering 2 meters every second. 
The object's velocity
starts at 2.0 m/s. It's velocity remains
at that value as time passes. 
The constant acceleration
is 0.0 m/s^{2}; so, the velocity
does not change as time passes. 

[2] XVA demonstration 
Comments:
[3]The object starts at the origin of its position number line.
At the start the object's velocity is 4.0 m/s, and it remains
at this value. Thus, the object moves away from the origin at
a constant speed in a positive direction. Since the velocity
of the object does not change, its acceleration is 0.0 m/s^{2}
throughout the motion.
Back
Parameters: 
x_{o}
= 0.0 m 
v_{o}
= 4.0 m/s^{ } 
a =
0.0 m/s^{2 } 



The object's position
starts at 0.0 m. It moves away from
the origin in a positive direction constantly
covering 4 meters every second. 
The object's velocity
starts at 4.0 m/s. It's velocity remains
at that value as time passes. 
The constant acceleration
is 0.0 m/s^{2}; so, the velocity
does not change as time passes. 

[3] XVA
demonstration 
Comments:
 This example is a lot like the one in [2], except here the constant positive velocity is
greater, as is the slope of the x
vs. t graph.
 See
Constant
Velocity Animate 1.
[4] The object starts at the origin of its
position number line. At the start the object's velocity is 6.0
m/s, and it remains at this value. Thus, the object moves
away from the origin at a constant speed in a positive
direction. Since the velocity of the object does not change,
its acceleration is 0.0 m/s^{2} throughout the motion.
Parameters: 
x_{o}
= 0.0 m 
v_{o}
= 6.0 m/s^{ } 
a =
0.0 m/s^{2 } 



The object's position
starts at 0.0 m. It moves away from the
origin in a positive direction constantly
covering 6 meters every second. 
The object's velocity
starts at 6.0 m/s. It's velocity remains
at that value as time passes. 
The constant acceleration
is 0.0 m/s^{2}; so, the velocity
does not change as time passes. 

[4] XVA demonstration 
Comments:
 This example is a lot like the ones in
[2]and [3], except here the
constant positive velocity is greater than either of those, and, so
is the slope of the x vs. t graph.
 See
Constant
Velocity Animate 1.
[5]The object starts at the origin of its position number line.
At the start the object's velocity is 2.0 m/s, and it
remains at this value. Thus, the object moves away from the
origin at a constant speed in a negative direction. Since the
velocity of the object does not change, its acceleration is 0.0
m/s^{2} throughout the motion.
Back
Parameters: 
x_{o}
= 0.0 m 
v_{o}
= 2.0 m/s^{ } 
a =
0.0 m/s^{2 } 



The object's position
starts at 0.0 m. It moves away from the
origin in a negative direction constantly
covering 2.0 meters every second. 
The object's velocity
starts at 2.0 m/s. It's velocity
remains at that value as time passes. 
The constant acceleration
is 0.0 m/s^{2}; so, the velocity
does not change as time passes. 

[5] XVA
demonstration 
Comments:
[6]The object starts at the origin of its position number line.
At the start the object's velocity is 4.0 m/s, and it
remains at this value. So, the object moves away from the
origin at a constant speed in a negative direction. Since the
velocity of the object does not change, its acceleration is 0.0
m/s^{2} throughout the motion.
Back
Parameters: 
x_{o}
= 0.0 m 
v_{o}
= 4.0 m/s^{ } 
a =
0.0 m/s^{2 } 



The object's position
starts at 0.0 m. It moves away from the
origin in a negative direction constantly
covering 4.0 meters every second. 
The object's velocity
starts at 4.0 m/s. It's velocity
remains at that value as time passes. 
The constant acceleration
is 0.0 m/s^{2}; so, the velocity
does not change as time passes. 

[6] XVA
demonstration 
Comments:
 This example is a lot like the one in [5], except here the constant negative velocity
is larger, or more negative, as
is the slope of the x vs. t graph.
 See
Constant
Velocity Animate 1.
[7] The object starts at the origin of its
position number line. At the start the object's velocity is 6.0
m/s, and it remains at this value. Thus, the object moves
away from the origin at a constant speed in a negative
direction. Since the velocity of the object does not change,
its acceleration is 0.0 m/s^{2} throughout the motion.
Parameters: 
x_{o}
= 0.0 m 
v_{o}
= 6.0 m/s^{ } 
a =
0.0 m/s^{2 } 



The object's position
starts at 0.0 m. It moves away from the
origin in a negative direction constantly
covering 6.0 meters every second. 
The object's velocity
starts at 6.0 m/s. It's velocity
remains at that value as time passes. 
The constant acceleration
is 0.0 m/s^{2}; so, the velocity
does not change as time passes. 

[7] XVA
demonstration 
Comments:
 This example is a lot like the ones in
[5]and [6], except here the
constant negative velocity is yet more negative than either of
those, and so is the slope of the x vs. t
graph.
 See
Constant
Velocity Animate 1.
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