1. Acceleration and Free fall
2017

2. Measuring Distance Meter – international unit for measuring distance.
1 mm
= 50 m

3. S = d/t Calculating Speed
Speed (S) = distance traveled (d) / the amount of time it took (t).
S = d/t

4. Average speed Speed is usually NOT CONSTANT
Ex. Cars stop and go regularly
Runners go slower uphill than downhill
Average speed = total distance traveled/total time it took.

5. Calculating Average Speed Problem # 1
It took me 1 hour to go 40 km on the highway. Then it took me 2 more hours to go 20 km using the streets.
Total Distance:
40 km + 20 km = 60 km
Total Time:
1 h + 2 h = 3 hr
Ave. Speed:
total d/total t = 60 km/3 h = 20 km/h

6. Velocity Velocity – the SPEED and DIRECTION of an object. Example:
An airplane moving North at 500 mph
A missile moving towards you at 200 m/s

7. Graphing Speed: Distance vs. Time Graphs Problem # 2
Denver
V = 200 km/hr towards Denver
X = 1200 km
T = 6 hours
Phoenix

8. Change in Velocity
Each time you take a step you are changing the velocity of your body.
You are probably most familiar with the velocity changes of a moving bus or car.
The rate at which velocity (speed or direction) changes occur is called acceleration.

9. aavg = Δv = vf - vi Acceleration Δt tf - ti
The rate of change of velocity in a given time interval is acceleration.
Formula
aavg = Δv = vf - vi
Δt tf - ti
average acceleration = Change in velocity .
Time Required for Change

10. Acceleration= final velocity- starting velocity
time
Change in velocity = final – starting velocity velocity
vf vi
Acceleration= change in velocity (Δv)

11. Calculation Practice # 3
Betty the shuttle bus driver slows to a stop with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to 0.0 m/s?
vf = 0 m/s
vi = 9.0 m/s
aavg = -1.8m/s2
Δt = ?
aavg = Δv = vf - vi
Δt tf - ti
Δt=5.0s

12. Types of acceleration Increasing speed Decreasing speed
Example: Car speeds up at green light
Decreasing speed
Example: Car slows down at stop light
Changing Direction
Example: Car takes turn (can be at constant speed)
screeeeech

13. Acceleration +/- Acceleration has direction and magnitude.
When velocity increases in the positive direction, acceleration increases.
Ex. Train increasing speed as it leaves.
When velocity is constant, acceleration is zero.
When velocity in the positive direction is decreasing the acceleration is negative.
Ex. Train slows as it approaches station.

14. Positive acceleration Negative acceleration

15. A constant acceleration produces a straight line or linear slope (rise/run). The slope of a non- linear velocity-time graph (rise/run) will predict an objects instantaneous acceleration. a = v/t

16. Question # 4
How can a car be accelerating if its speed is a constant 65 km/h?
If it is changing directions it is accelerating

17. Calculating Acceleration Problem # 5
Vf = 16 m/s
Vi = 0 m/s
t = 4 s
A = ?
0 s
1 s
2 s
3 s
4 s
0 m/s
4 m/s
8 m/s
12 m/s
16 m/s

18. 4 Kinematic Equations

19. Δx = displacement (final position – initial position)
vf = velocity or speed final
vi = initial velocity or speed
t = time
a = acceleration

20. Calculation Practice # 6
Erica reaches a speed of 42 m/s. She then begins a uniform negative acceleration, using its parachute and brakes. She comes to rest 5.5s later. How far has the dragster traveled while stopping?
vi = 42 m/s vf = 0 m/s
Δt = 5.5s Unknown Δx = ?
X = m

21. Galileo Galilei ( )
Father of Kinematics (How)
Concluded that all objects fall at same rate of acceleration.
Demonstrated the scientific method in developing the kinematics of free fall motion.
Tested his hypothesis through experimentation.

22. Galileo
He found that the distance depended on the square of the time and that the velocity increased as the ball moved down the incline.
The relationship was the same regardless of the mass of the ball used in the experiment.

23. https://www.youtube.com/watch?v=V6xqgWVgAok free fall
ball drop
An object in free-fall is only subject to the force of gravity (weight)
(Neglect Air Resistance)
coaster
plane

24. Freely falling objects have constant acceleration.
This is only true with the absence of air resistance.
The free-fall acceleration is denoted with the symbol g and is equal to -9.8m/s2.

25. Free Fall acceleration is directed downwards, toward the center of the Earth.
Since the downwards direction is negative, the acceleration due to gravity is also considered negative.

26. Important!
Since the acceleration of gravity is down,
when in free-fall, ignoring air resistance:
a = g = m/s2

27. All objects, when thrown up will continue to move upward for some time, stop momentarily at the peak, and then change direction and begin to fall.
At that moment
velocity is 0 but
acceleration is
always -9.8 m/s/s.

28. Freely Falling Body
Since accelerating objects are constantly changing their velocity, you can say that the distance traveled divided by the time taken to travel that distance is not a constant value.
A falling object for instance usually accelerates as it falls.
The fact that the distance which the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward

29. Distance and time are
Given. You can see it is accelerating at a constant rate because more distance is covered each time.V is increasing
Velocity and time are given and a = v/t. Acceleration on earth is always -9.8 m/s/s. (rounded to 10 here)

30. Which object hits the ground first? (ignore air friction)
Which object hits the ground first when we include air friction?

31. No Air Resistance
With Air Resistance

32. Terminal Velocity?
Well, eventually, the force of air resistance becomes large enough to balance the force of gravity. At this instant in time the object stops accelerating. The object is said to have "reached a terminal velocity."

33. Basically the more massive object accelerates longer
In situations in which there is air resistance, massive objects fall faster than less massive objects. Why?
Massive objects fall faster than less massive objects because they are acted upon by a larger force of gravity; for this reason, they accelerate to higher speeds until the air resistance force equals their gravity force.
Basically the more massive object accelerates longer
before reaching terminal velocity.

34. Practice #7
A tennis ball is thrown vertically upward with an initial velocity of 8m/s. What is the ball’s speed when it returns to the starting point? How long will it take?
Knowns?
a = -9.8 m/s/s, vi = 8m/s, vf(top) = 0 m/s, vitop = 0 m/s
Unknowns?
vf bottom= ?, t = ?
Equation?
Vf = vi +at
0 = t, 8/-9.8 = .82 sec to top x 2 = 1.6 s
Now vitop = 0 m/s and vfbottom = ?; vfbottom = 0 + (-9.8).82 = -8m/s

35. Practice # 8
#4. Stephanie hits a volleyball from a height of .8m and gives it an initial velocity of 7.5m/s straight up. How high will the ball go? How long will it take to get to that height?
Knowns?
Vi = 7.5 m/s, vf = 0 m/s, a = -9.8 ms/s/s
Unknowns?
X = ?, t = ?
Equation?
Vf = vi +at
0 = 7.5 +(-9.8t); t = .76 s
X = .5(vi+vf)t = .5(7.5).76 = = m