1. Kinematics
AP Physics 1

2. Displacement Displacement (x or y) "Change in position"
It is not necessarily the total distance traveled. In fact, displacement and distance are entirely different concepts. Displacement is relative to an axis.
"x" displacement means you are moving horizontally either right or left.
"y" displacement means you are moving vertically either up or down.
The word change is expressed using the Greek letter DELTA ( Δ ).
To find the change you ALWAYS subtract your FINAL - INITIAL position
It is therefore expressed as either   Δx = xf - xi or Δy = yf - yi
Distance - How far you travel regardless of direction.

3. Example
Suppose a person moves in a straight line from the lockers( at a position  x = 1.0 m) toward the physics lab(at a position x = 9.0 m) , as shown below
The answer is positive so the person must have been traveling horizontally to the right.

4. Example Suppose the person turns around!
The answer is negative so the person must have been traveling horizontally to the left
What is the DISPLACEMENT for the entire trip?
What is the total DISTANCE for the entire trip?

5. Average Velocity
Velocity is defined as: “The RATE at which DISPLACEMENT changes”. Rate = ANY quantity divided by TIME.
Average SPEED is simply the “RATE at which DISTANCE changes”.

6. Example
A quarterback throws a pass to a defender on the other team who intercepts the football. Assume the defender had to run 50 m away from the quarterback to catch the ball, then 15 m towards the quarterback before he is tackled. The entire play took 8 seconds.
Let's look at the defender's average velocity:
“m/s” is the derived unit for both speed and velocity.
Let's look at the defender's speed:

7. Average Acceleration
Acceleration is the RATE at which VELOCITY changes.
A truck accelerates from 10 m/s to 30 m/s in 2.0 seconds. What is the acceleration?
Suppose the same truck then slows down to 5 m/s in 4 seconds. What is the acceleration?
“m/s/s” or “m/s2” is the derived unit for acceleration.

8. What do the “signs”( + or -) mean?
Quantity
Positive
Negative
Displacement
You are traveling north, east, right, or in the +x or +y direction.
You are traveling south, west, left, or in the –x or –y direction.
Velocity
The rate you are traveling north, east, right, or in the +x or +y direction.
The rate you are traveling south, west, left, or in the –x or –y direction.
Acceleration
Your velocity(speed) is increasing in a positive direction or your speed is decreasing in a negative direction.
Your velocity(speed) is decreasing in a positive direction or your speed is increasing in a negative direction.

9. Beware – the signs can confuse!
Suppose a ball is thrown straight upwards at 40 m/s. It takes 4 seconds to reach its maximum height, then another 4 seconds back down to the point where it was thrown. Assume it is caught with the same speed it was thrown. Calculate the acceleration upwards and downwards.
This negative sign came from using the DELTA
This negative sign came from the DIRECTION of the velocity.
It is no surprise you get a negative answer both ways as gravity acts DOWNWARDS no matter if the ball goes up or down. It is GRAVITY which changes the ball’s velocity.

10. Defining the important variables
Kinematics is a way of describing the motion of objects without describing the causes. You can describe an object’s motion:
In words Mathematically Pictorially Graphically
No matter HOW we describe the motion, there are several KEY VARIABLES that we use.
Symbol
Variable
Units t
Time s a
Acceleration
m/s/s
x or y
Displacement m vo
Initial velocity
m/s v
Final velocity
g or ag
Acceleration due to gravity

11. The 3 Kinematic equations
There are 3 major kinematic equations than can be used to describe the motion in DETAIL. All are used when the acceleration is CONSTANT.

12. Kinematic #1

13. Kinematic #1
Example: A boat moves slowly out of a marina (so as to not leave a wake) with a speed of 1.50 m/s. As soon as it passes the breakwater, leaving the marina, it throttles up and accelerates at 2.40 m/s/s.
a) How fast is the boat moving after accelerating for 5 seconds?
What do I know?
What do I want?
vo= 1.50 m/s
v = ?
a = 2.40 m/s/s
t = 5 s
13.5 m/s

14. Kinematic #2
b) How far did the boat travel during that time?
37.5 m

15. Does all this make sense?
13.5 m/s
1.5 m/s
Total displacement = = 37.5 m = Total AREA under the line.

16. Interesting to Note A = HB
Most of the time, xo=0, but if it is not don’t forget to ADD in the initial position of the object.
A=1/2HB

17. Kinematic #3 What do I know? What do I want? vo= 12 m/s x = ?
Example: You are driving through town at 12 m/s when suddenly a ball rolls
out in front of your car. You apply the brakes and begin decelerating at
3.5 m/s/s.
How far do you travel before coming to a complete stop?
What do I know?
What do I want?
vo= 12 m/s
x = ?
a = -3.5 m/s/s
V = 0 m/s
20.57 m

18. Common Problems Students Have
I don’t know which equation to choose!!!
Equation
Missing Variable x v t

19. Kinematics for the VERTICAL Direction
All 3 kinematics can be used to analyze one dimensional motion in either the X direction OR the y direction.

20. “g” or ag – The Acceleration due to gravity
The acceleration due to gravity is a special constant that exists in a VACUUM, meaning without air resistance. If an object is in FREE FALL, gravity will CHANGE an objects velocity by 9.8 m/s every second.
The acceleration due to gravity:
ALWAYS ACTS DOWNWARD
IS ALWAYS CONSTANT near the surface of Earth

21. Examples
A stone is dropped at rest from the top of a cliff. It is observed to hit the ground 5.78 s later. How high is the cliff?
What do I know?
What do I want?
voy= 0 m/s
y = ?
g = -9.8 m/s2
yo=0 m
t = 5.78 s
Which variable is NOT given and
NOT asked for?
Final Velocity! m
H =163.7m

22. Examples
A pitcher throws a fastball with a velocity of 43.5 m/s. It is determined that during the windup and delivery the ball covers a displacement of 2.5 meters. This is from the point behind the body when the ball is at rest to the point of release. Calculate the acceleration during his throwing motion.
Which variable is NOT given and
NOT asked for?
What do I know?
What do I want?
vo= 0 m/s
a = ?
x = 2.5 m
v = 43.5 m/s
TIME
378.5 m/s/s

23. Examples
How long does it take a car at rest to cross a 35.0 m intersection after the light turns green, if the acceleration of the car is a constant 2.00 m/s/s?
What do I know?
What do I want?
vo= 0 m/s
t = ?
x = 35 m
a = 2.00 m/s/s
Which variable is NOT given and
NOT asked for?
Final Velocity
5.92 s

24. Examples
A car accelerates from 12.5 m/s to 25 m/s in 6.0 seconds. What was the acceleration?
What do I know?
What do I want?
vo= 12.5 m/s
a = ?
v = 25 m/s
t = 6s
Which variable is NOT given and
NOT asked for?
DISPLACEMENT
2.08 m/s/s

25. Scalar Scalar Example Magnitude Speed 20 m/s Distance 10 m Age
15 years
Heat
1000 calories
A SCALAR is ANY quantity in physics that has MAGNITUDE, but NOT a direction associated with it.
Magnitude – A numerical value with units.

26. Vector
A VECTOR is ANY quantity in physics that has BOTH MAGNITUDE and DIRECTION.
Vector
Magnitude & Direction
Velocity
20 m/s, N
Acceleration
10 m/s/s, E
Force
5 N, West
Vectors are typically illustrated by drawing an ARROW above the symbol. The arrow is used to convey direction and magnitude.

27. Applications of Vectors
VECTOR ADDITION – If 2 similar vectors point in the SAME direction, add them.
Example: A man walks 54.5 meters east, then another 30 meters east. Calculate his displacement relative to where he started? +
54.5 m, E
30 m, E
Notice that the SIZE of the arrow conveys MAGNITUDE and the way it was drawn conveys DIRECTION.
84.5 m, E

28. Applications of Vectors
VECTOR SUBTRACTION - If 2 vectors are going in opposite directions, you SUBTRACT.
Example: A man walks 54.5 meters east, then 30 meters west. Calculate his displacement relative to where he started?
54.5 m, E -
30 m, W
24.5 m, E

29. Non-Collinear Vectors
When 2 vectors are perpendicular, you must use the Pythagorean theorem.
A man walks 95 km, East then 55 km, north. Calculate his RESULTANT DISPLACEMENT.
Finish
The hypotenuse in Physics is called the RESULTANT.
55 km, N
Vertical Component
Horizontal Component
Start
95 km,E
The LEGS of the triangle are called the COMPONENTS

30. BUT……what about the direction?
In the previous example, DISPLACEMENT was asked for and since it is a VECTOR we should include a DIRECTION on our final answer. N
W of N
E of N
N of E
N of W W E
N of E
S of W
S of E
NOTE: When drawing a right triangle that conveys some type of motion, you MUST draw your components HEAD TO TOE.
W of S
E of S S

31. BUT…..what about the VALUE of the angle???
Just putting North of East on the answer is NOT specific enough for the direction. We MUST find the VALUE of the angle.
To find the value of the angle we use a Trig function called TANGENT.
109.8 km
55 km, N q
N of E
95 km,E
So the COMPLETE final answer is : km, 30 degrees North of East

32. What if you are missing a component?
Suppose a person walked 65 m, 25 degrees East of North. What were his horizontal and vertical components?
The goal: ALWAYS MAKE A RIGHT TRIANGLE!
To solve for components, we often use the trig functions sine and cosine.
H.C. = ?
V.C = ? 25
65 m

33. Example 23 m, E - = 12 m, W - = 14 m, N 6 m, S 20 m, N 35 m, E R
A bear, searching for food wanders 35 meters east then 20 meters north. Frustrated, he wanders another 12 meters west then 6 meters south. Calculate the bear's displacement.
23 m, E - =
12 m, W - =
14 m, N
6 m, S
20 m, N
35 m, E R
14 m, N q
23 m, E
The Final Answer: m, 31.3 degrees NORTH of EAST

34. Example
A boat moves with a velocity of 15 m/s, N in a river which flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north.
8.0 m/s, W
15 m/s, N Rv q
The Final Answer : degrees West of North

35. Example
A plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate the plane's horizontal and vertical velocity components.
H.C. =? 32
V.C. = ?
63.5 m/s

36. Example
A storm system moves 5000 km due east, then shifts course at 40 degrees North of East for 1500 km. Calculate the storm's resultant displacement.
1500 km
V.C. 40
5000 km, E
H.C.
5000 km km = km R
964.2 km q
The Final Answer: degrees, North of East km