1. Chapter 2

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.

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.

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.

12. vf = vi + at d = vavt vav = (vf + vi)/2 d = vit + 1/2at2
Constant
vf = vi + at
t = time
d = displacement
d = vavt
vi = initial velocity
vav = (vf + vi)/2
vav = average
velocity
d = vit + 1/2at2
a = acceleration
vf2 = vi2 + 2ad
vf = final velocity

13. Graphing and Gravity

14. Gravity
Gravity is defined as a force exerted on all objects within an objects atmosphere.
All objects have mass, this doesn’t EVER change.
The force of gravity causes an object to have weight. The weight of an object depends on the force of gravity being exerted.
This weight is also known as inertia.
This means that an objects weight and its inertia are equal.

15. Calculating Gravity
On the surface of the earth, the acceleration due to gravity equals 9.81m/s2.
As you move closer to the center of the earth, this number would increase, farther away and it would decrease

16. Calculating Gravity
When you leave the earth’s atmosphere, gravity no longer has an effect, therefore the object is “weightless”. It still has mass, but it has no inertia.
The acceleration due to gravity is different on different planets. It can be calculated using this formula:
Fg=mg Fg= force of gravity m= mass of object
g= acceleration due to gravity

17. Sample Problem
An object weighs 15N on Planet X and has a mass of 3kg. What is the acceleration due to gravity on Planet X?
Fg= mg
15N=3kg(g)
g=5mls2
*note: N= newtons, a unit of force/ weight

18. “g” Force Different types of motion can affect “g” in various ways.
Roller Coasters
Rapid ascents and descents on rides can add or subtract “g”s
Moving quickly uphill increases the force of gravity by increasing the acceleration
This increased “g” will cause you to be pressed into your seat
This also happens to astronauts as they “blast off”
Too many “g”s and the force will cause the body to cave in
A rapid descent downhill causes negative “g”s this will cause the body to feel weightless (airtime)

19. 2. Elevators
The same positive and negative “g”s can be felt on a moving elevator.
Rising rapidly will cause an increase in “g”s.
Falling rapidly will cause a state of weightlessness.

20. Using “g” in equations
When solving problems involving gravity, the value of g may be substituted for a in any equation.
Examples:
a = v/t becomes
g= v/t
d= 1/2 at2 becomes d= ½ gt2
v2 = 2ad becomes v2= 2gd

21. Sample problems g=v/t 9.81mls2 = v/4s
An object falls from a cliff a distance of 30m before it hits the ground. How long did it fall for?
d=30m
g=9.81mls2
d=1/2gt2
30m=1/2(9.81mls2)(t2)
t=2.5s
An object is in free-fall for 4 seconds. What speed does it reach?
t= 4 seconds
g= 9.81 mls2
g=v/t
9.81mls2 = v/4s
V=39.2 mls

22. II: Graphing Motion: Slope
Slope is defined in many ways.
It can be the change in (y) divided by the change in (x)
It is also known as “rise over run”
It is not difficult to calculate: use the formula
Slope =(y2-y1)/(x2-x1)
Choose any two points on your graph to make your calculation. It is often helpful to use the origin (0,0) as one of the points.

23. Applying the slope concept to graphs of motion
In physics, a slope calculation doesn’t just yield a number, it actually is a measurable quantity
We will concentrate on calculating slopes for distance/time and velocity/time graphs

24. Slope of a distance/time graph
To show the meaning of the slope in this graph, we will include the units in our calculation.
We will choose the origin (0,0) and (5,10) for our calculation.
Slope=y/x
10m-0m/5s-0s
10m/5s
2 m/s
Please note that by calculating the slope, you have calculated the velocity of the object for that interval of the graph.
Please memorize: The slope of a distance/time graph is a measure of the object’s velocity.

25. Slope of a velocity/time graph
We will repeat the slope calculation with the new graph
Slope=y/x
30m/s-0m/s
20s - 0s
(30m/s) / 20s
1.5 m/s2
In this example we have calculated the acceleration of the object for that interval of the graph
Please memorize: The slope of a velocity/time graph is a measure of the object’s acceleration

26. Interpreting the data presented in graphs
Distance/time graphs
Most times, you will see graphs in two forms, either a simple single line graph, or a complete trip sketched out
Each graph can be interpreted either by looking at the trends in the data, or by looking at the slope.

27. Simple distance/time graphs
Conclusion: object is at rest (slope=0)
Conclusion: object is moving with constant velocity (slope is constant)

28. More simple graphs
Object is accelerating (slope is changing)-note the line is curved

29. Simple velocity/time graphs
Conclusion: object is moving at constant speed (slope=0)
This distance/time graph matches the velocity/time graph on the left

30. Here’s another one
Conclusion: object has a constant acceleration (slope is steady)
This graph matches the one on the left

31. One more
Velocity is changing, acceleration is changing (slope is changing)