2. The position of any object must be given
with respect to some reference point.
An object’s position is its directed
distance from a reference point.
Movement
is said to have occurred when
the position of an object with
respect to a given
reference point has changed.

3. This change in position of an object is often called its displacement.
Displacement, then, is a vector quantity.
Distance, or length, is a scalar.
Click here to explore differences between
distance and displacement.
Click here to make calculations and
here to check your understanding.

4. In one dimensional motion, the displacement direction is often given
as positive, +, or negative, -.
A displacement of +3.5 m implies movement of
3.5 m in the positive direction.
A displacement of -3.5 m implies movement of
3.5 m in the negative direction.
Positive and negative directions are
chosen arbitrarily, but usually agree with
standard mathematical conventions.

5. vav t d = vav = average velocity;
The average velocity of an object is defined to
be the ratio of its change in position to the
time taken to change the position. d
vav = t
vav = average velocity;
in units of m/s, mph, ft/s, km/hr, etc...
d = change in position, or displacement;
in units of m, in, ft, km, mi, etc...
t = change in time;
in units of s, min, hr, etc...

6. The “sign” of the velocity indicates the direction of movement.
A positive sign indicates movement
in the positive direction.
A negative sign indicates movement
in the negative direction.

7. Speed is the magnitude of velocity.
It is a scalar and has no direction given with it.
Average speed is the total distance traveled
divided by the total time taken.
Average velocity is the total displacement
divided by the total time taken.
Average speed and average velocity are
generally not equivalent because total distance
and total displacement are generally not the same.
When would they have the same magnitudes?

8. Speed is the absolute value of velocity.
It is always a positive value.
If an object increases its speed while traveling in
the negative direction, its velocity actually decreases.
If an object decreases its speed while traveling in
the negative direction, its velocity actually increases.

9. aav t v = aav = average acceleration; v = change in velocity;
The average acceleration of an object is defined
to be the ratio of its change in velocity to the
time taken to change the velocity. v
aav = t
aav = average acceleration;
in units of m/s/s, mph/s, ft/s/s, km/hr/s, etc...
v = change in velocity;
in units of m/s, in/s, ft/s, km/hr, mph, etc...
t = change in time;
in units of s, min, hr, etc...

10. The “sign” of the acceleration indicates whether the velocity is
increasing or decreasing.
A positive sign indicates that the velocity
is increasing. It will also be an increase in
speed if the object is traveling in the positive
direction. It is a decrease in speed otherwise.
A negative sign indicates that the velocity
is decreasing. It will also be a decrease in
speed if the object is traveling in the positive
direction. It is an increase in speed otherwise.

11. It is important to note that information about an object’s
acceleration tells us how the object’s velocity is changing.
In order to know what this change in velocity
is doing to the object’s speed, we must
know the direction the object is traveling.
As a rule, if the object’s velocity and acceleration
are in the same direction (have the same sign),
we can say that the object’s speed is increasing.
If the velocity and acceleration are in opposite
directions (have opposite signs), we know
that the object’s speed is decreasing.
What can we say about changes in speed and/or velocity
if the acceleration is either increasing or decreasing?

12. vf = vi + at d = vavt vav = (vf + vi)/2 d = vit + 0.5at2
Constant
vf = vi + at
t = time
d = displacement
d = vavt
vi = initial velocity
vav = (vf + vi)/2
vav = average
velocity
d = vit + 0.5at2
a = acceleration
vf2 = vi2 + 2ad
vf = final velocity

13. You can learn more about distance, displacement, speed, velocity,
relative velocity, and acceleration
by clicking on these simulation links:
link1, link2, link3, link4, link5

14. Position – Time Graphs Summarized
the y-coordinate at any time gives the position of the object
the slope of a position-time graph at any instant is the instantaneous
velocity of the object
horizontal graph segments indicate that the object is “at rest”
graph segments moving upward imply movement in the positive
direction
graph segments moving downward imply movement in the negative
straight line graph segments indicate constant speed
curving graph segments indicate changing speed
graph segments becoming steeper indicate an increase in speed
graph segments becoming less steep indicate a decrease in speed
a change of direction is indicated whenever the graph is concave
upward or downward

15. Velocity – Time Graphs Summarized
the y-coordinate at any time gives the velocity of the object
the slope of a velocity-time graph is the acceleration of the object
horizontal graph segments indicate that the object has constant
velocity
graph segments above the x-axis imply movement in the positive
direction
graph segments below the x-axis imply movement in the negative
horizontal segments on the x-axis indicate no movement
straight line graph segments indicate constant acceleration
graph segments moving upward indicate an increase in velocity
graph segments moving downward indicate a decrease in velocity
a change of direction is indicated whenever the graph crosses the x-
axis
an increase in speed is indicated by graph segments moving away
from the x-axis

16. Acceleration – Time Graphs Summarized
the y-coordinate at any time gives the acceleration of the object
horizontal graph segments indicate that the object has constant
acceleration
a horizontal graph segment on the x-axis indicates that the object
has constant velocity (no acceleration)
graph segments above the x-axis imply increasing velocities
graph segments below the x-axis imply decreasing velocities
no changes in direction may be inferred from these graphs
At the introductory physics level, we typically only deal with constant acceleration situations, so acceleration graphs generally consist of horizontal segments only.