1. Motion in One Dimension
Golden Valley HS Physics Mr. Campbell

2. 2-1 Displacement and Velocity
Motion
Motion is what happens all around us.
Different directions and different speeds.
It requires a special effort to analyze motion as a physicist does.

3. One-dimensional motion is the simplest form of motion
One way to simplify motion is to consider it only in one direction.
Think of a commuter train on a straight track.
It can only move forward or backward.

4. Motion takes place over time and depends upon the frame of reference
Describing the motion of a train is simple.
Earth is spinning on an axis, moving around the sun and our sun is moving inside of a galaxy.
To help simplify what we are studying we can use a frame of reference. It is a point that stays fixed.
The gecko’s motion is measured along the x axis using centimeters.
Motion

5. Displacement Displacement is a change in position
The initial position to the final position is called the displacement of the object.
The gecko starts at xi and moves to xf.
The Greek letter (Δ) “delta” shows change.
Displacement can also be shown vertically
with the y axis.
Displacement

6. Displacement is not always equal to the distance traveled
If the gecko runs up the tree as shown, the change in displacement is simply yf – yi or 60 cm.
If the gecko moves back down to 50 cm,
50 cm – 20 cm = 30 cm of total displacement
(based on the starting point).
If the gecko returns to its starting point its total displacement will be “0”.

7. Displacement can be positive or negative
In the below example there are only two directions our object can move.
Right will be considered east or positive x. Left will be west or negative x.
Up with be north(positive y) down will be south(negative y)

8. Velocity
Where an object starts and where it stops does not completely describe its motion.
The ground you are standing on may be moving to the left at 2 cm per year (plate tectonics).
If there is an earthquake, we could move 10 cm in a second!

9. Average velocity is displacement divided by the time interval
Average velocity is the displacement divided by the time interval.
The S.I. unit is meters per second (m/s)
This value is an average.
You may have stopped for a while, traveled slower or faster for a bit.
Velocity

10. Practice A: Average Velocity and Displacement
During a race on level ground, Andra runs with an average velocity of 6.02 m/s to the east. What is Andra’s displacement after 137 s? 
answer
825 m to the east

11. Velocity is not the same as speed
Speed and velocity sometimes are used interchangeably.
In Physics they are different.
Velocity describes the magnitude of that motion and direction.
Speed however, has no direction only magnitude.

12. Velocity can be interpreted graphically
Velocity can be plotted on a graph.
Position is normally plotted on the vertical axis and time on the horizontal.
If we have constant velocity, we will have a straight line

13. This graph shows… Object 1: positive slope = positive velocity
Object 2: zero slope = zero velocity
Object 3: negative slope = negative velocity
Sign Conventions

14. Instantaneous velocity may not be the same as average velocity
This graph show changing velocity with time.
This causes a curved line on our graph.
Any single point on this graph shows instantaneous velocity.
The instantaneous velocity at a given time can be determined by measuring the slope of the line that is tangent to that point on the position-versus-time graph.
The slope and shape of a graph of acceleration describe the object’s motion.

15. 2.1 Questions 1. What is a frame of reference? _____________________ 2. The Greek letter (Δ) “delta” shows ________ 3. T / F Displacement is always equal to distance traveled. 4. Average velocity is the displacement divided by __________ 5. Speed has no direction, only __________
The part that does not move
change
False
time
magnitude

16. Sec 2-2 Acceleration Changes in Velocity
Acceleration is the rate of change of velocity with respect to time
A bus approaches a stop and begins to apply the brakes.
The speed changes from 9.0 m/s to 0 m/s in over a period of 5 seconds.
If a dog were to run out and the bus stopped in 1.5 s, these two stops would be very different for the passengers.

17. The rate of change of velocity in a given time is called acceleration.
The magnitude of average acceleration is found by dividing the total change in velocity by the time it takes.
The S.I. unit is the meter per second per second (m/s2) or how much the velocity changes each second.
Changes in Velocity

18. Practice B: Average Acceleration
A shuttle bus slows down with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop?
Given: vi = 9.00 m/s vf = 0 m/s aavg = -1.8 m/s2 
Answer
5.0 s

19. Acceleration has direction and magnitude
Velocity is positive when a train moves to the right.
If the velocity increase as it travels in this direction, the final velocity will be greater than when it started.
When change in “v” is positive, acceleration is also positive.
On long trips the train may stay at constant velocity for a while. If velocity is not changing Δv = 0 m/s. Therefore acceleration is zero.
When the train slows down, its velocity
is still positive but changing.
Because initial velocity is greater than
final. Acceleration is negative.

20. The slope and shape of the graph describe the object’s motion
Looking at this graph, we can see the speed of the train is increasing over time.
“A” shows we have both positive direction and acceleration.
“B” shows positive direction and constant speed – no acceleration.
“C” shows continued positive
direction but negative acceleration.

21. If the train were moving backward (negative direction) and speeding up, we could have negative acceleration also.
When looking at this table, take into consideration which way the train is moving.
If vi is (-) then the train is moving backward.

22. Motion with Constant Acceleration
This photo was taken with a strobe light flashing every 0.1 second.
Gravity accelerates things as they fall. This object is undergoing constant acceleration.
Since its speed changes with time, it covers a greater distance in each constant time interval.

23. Displacement depends on acceleration, initial velocity and time
This graph shows an object with
constant acceleration is going
faster with time.
With constant acceleration, average velocity is equal to the average between initial and final velocity. 
To find displacement, we substitute x and t into the equation. This equation makes finding displacement easier.

24. Practice C: Displacement with Constant Acceleration
A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to a rest 5.5 seconds later.
Find the distance that the car travels during braking.
Answer
120 m

25. Final velocity depends on initial velocity, acceleration and time
You can use this equation to find final velocity of an object after it has accelerated at a constant rate for any time interval.
For displacement of an object use…
This can be used to find displacement and a certain speed after a displacement has been reached.

26. Practice D: Velocity and displacement with uniform acceleration
A plane starting from rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15 s before takeoff.
What is its speed at takeoff?
Answer
How long must the runway be for the plane to be able to take off?
72 m/s
540 m

27. Final velocity depends on initial velocity, acceleration and displacement
So far our equations for acceleration have required a time interval.
Now we will rearrange the equation, substituting time to find distance or displacement.
This new equation gives us final velocity after a displacement…
When using tis equation, you must take the square root of the right side to find final velocity.

28. Practice E: Final velocity after any displacement
A person pushing a stroller starts from rest, uniformly accelerating at a rate of m/s2.
What is the velocity of the stroller after it has traveled 4.75 m?
Given: vi = 0 m/s a = m/s2 Δx = 4.75 m
vf = ? 
Answer
+2.18 m/s

29. The equations you have just used are summarized below.
They can also be referenced on P. 58 of you textbook.
If the object starts from rest (vi = 0) you can you the formulas on the right.

30. 2.2 Questions 1. Acceleration is the rate of change of _________ with respect to time. 2. Acceleration has direction and __________ 3. When a train slows down, its velocity is still __________ but changing. 4. Gravity __________ things as they fall. 5. T / F If we have final velocity, initial velocity and acceleration, we can calculate time.
velocity
magnitude
positive
accelerates
True

31. Sec 2-3 Falling Objects Free Fall
In 1971, astronaut David Scott showed on the moon (a vacuum), a hammer and a feather will fall at the same rate in the absence of air resistance.
Both objects hit the moon’s surface at the same time.

32. Freely falling bodies undergo constant acceleration
What goes up must come down
Freely falling bodies undergo constant acceleration
In a vacuum chamber, any two objects will fall exactly at the same rate.
In the photo you can see the time interval is the same but the displacement keeps changing.
This shows the objects are accelerating.
This constant acceleration is called free fall.
The magnitude of acceleration due to gravity (g) is m/s2.
This acceleration is directed downward, therefore it is negative.
Freely fall constant acceleration

33. Acceleration is constant during upward and downward motion
The object shown in this strobe light photo goes up, slows, changes direction and falls.
The acceleration on the object is negative the entire time. Even when the object is going up, it experiences a force (gravity) pulling it down.
If it were not for this negative acceleration (gravity), the ball would travel up continuously.

34. This graph shows gravity’s negative acceleration plotted with change in velocity.
Because acceleration is negative, it continually slopes down to the right.
Objects thrown upward same acceleration as falling.

35. Freely falling objects always have the same downward acceleration
It may seem confusing to think an object moving up is undergoing a negative acceleration.
When an object is moving down it has negative velocity and negative acceleration, therefore it is going faster with time.
When it is thrown up, it has positive velocity but negative acceleration so it is slowing down.

36. Practice F: Falling Object
Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upward.
If the volleyball starts from 2.0 m above the floor, how long will it be in the air before it strikes the floor?
Given: vi = +6.0 m/s ag = m/s2 Δy = -2.0 m 
Answer When ball hits the floor, next 
-8.7 m/s

37. …to figure out the overall time the ball was in the air, we use…  Answer This the time it took the ball to go up, go down and then another 2 meters.
1.50 s

39. 2.3 Questions 1. In the absence of air, all objects fall at the same ______ 2. Free falling objects undergo constant ________ 3. T / F Acceleration is constant during upward and downward motion. 4. Objects thrown up have positive velocity but negative acceleration, this causes them to ______ down.
rate
acceleration
True
slow

40. End