1. Motion in one dimension
Test 2

2. Kinematics
- the branch of physics that describes motion in terms of x, v, a, and t
x- position (m) (sometimes d)
v- velocity (m/s)
a- acceleration (m/s²)
t- time (s)
Dynamics is kinematics + force exerted on an object.

3. Displacement Defined as the change in position
f stands for final and i stands for initial
Units are meters (m) in SI
Example: If Xf = 30m and Xi = 20m what is the displacement?

4. Distance is different than Displacement
Distance is a scalar quantity which refers to "how much ground an object has covered" during its motion.
Displacement is a vector quantity which refers to "how far out of place an object is"; it is the object's overall change in position.

5. A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.
Distance traveled would be 2m +4m + 2m +4m = 12m
Displacement would be 0m, you end where you started.

6. Displacement
Xi =120m Xf = 5m ΔX= Xf - Xi ΔX= 5-120= -115 Negative displacement moves left or down; positive displacement moves right or up.

7. Displacement Examples
From A to B
xi = 30 m
xf = 52 m
x = 22 m
The displacement is positive, indicating the motion was in the positive x direction
From C to F
xi = 38 m
xf = -53 m
x = -91 m
The displacement is negative, indicating the motion was in the negative x direction

8. Position versus time graphs

9. Speed
The average speed of an object is defined as the total distance traveled divided by the total time elapsed (scalar quanity)
SI units are m/s (meters per second)
Always positive

10. Velocity Velocity is magnitude and direction
7 m/s East
If V is positive motion is to the right.
If V is negative motion is to the left.
Speed is the magnitude of velocity (no direction)
Velocity is a vector quanity

11. Velocity It takes time for an object to undergo a displacement
The average velocity is the rate at which the displacement occurs
Velocity can be positive or negative
t is always positive

12. Speed vs. Velocity
Cars on both paths have the same average velocity since they had the same displacement in the same time interval
The car on the blue path will have a greater average speed since the distance it traveled is larger

13. Practice problem
How fast is a train moving if it travels 25 m in 5 sec?
Given:
Solve:
X=25m
V = x/t
V = 25m / 5 sec
t=5s
V = 5 km/s

14. Example Question
If a car travels 100 miles in 2 hours what is the velocity of the car?
________ mph
Convert this is meters/second

15. Example question
A car travels 40 meters between the hours of 10am and 12am. What is the cars average velocity?

16. A runner runs 3 seconds at 4m/s, stops for one second, and begins running for 2 seconds and covers 3m.
What is the velocity from (a) A to B, (b) B to C, and (c) A to D

17. Constant Velocity • Constant velocity is when an object’s
velocity remains the same for a given
amount of time.
• An objects current velocity would be equal to the average velocity.

18. Acceleration Changing velocity means an acceleration is present
Acceleration is the rate of change of the velocity
Units are m/s²
The units come from m/s/s

19. Which car has the greatest acceleration?
Blue
Blue = A, Red = B, Green = C
Which line goes with which car?

20. Practice problem Given: Solve: a = vf – vi t 5s = t a = 6 m/s2
What is the acceleration of a car that travels from 20m/s to 50m/s in a period of 5s?
Given:
Solve:
a = vf – vi t
20m/s = vi
50 m/s =vf
a = 50m/s – 20m/s 5s
5s = t
a = 6 m/s2

21. Velocity vs acceleration

22. We know that
Vf= Vi + aΔt

23. You need to understand that..
Xo = Xi
X= Xf

24. Motion in One Dimension with Constant Acceleration
V= Vo + at
X – Xo= ½ (v + vo)t
X – Xo= Vo t + ½ at2
V2 - Vo2 = 2a (X – Xo)

25. Freely Falling Objects (3.3)
An object moving under the influence of gravity alone. Regardless of its initial conditions.

26. Freely Falling objects
Drop something
Throw something and let it fall
Throw something down
Objects thrown upward or downward and those released from rest are all falling freely once released.
Once in freefall motion all objects experience the same acceleration; downward and equal to the acceleration due to gravity. (Earths Gravity= 9.8 m/s²

27. V= Vo - gt y – yo= ½ (v + vo)t y – yo= Vo t - ½ gt2
a= -g = 9.8 m/s²
V= Vo - gt
y – yo= ½ (v + vo)t
y – yo= Vo t - ½ gt2
V2 - Vo2 = - 2g (y – yo)

29. Remarks…
Air resistance is neglected. All objects regardless of there mass will move at the same rate if they have the same initial conditions
Free fall motion is symetrical

30. JD drops a pile of roof shingles from the top of a roof located 8
JD drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground.
Given: vi = 0.0 m/s
y = –8.52 m
a = –9.8 m/s2
Find: t = ??
y-y. = v.t + 1/2gt2
-8.52m = (-9.8m/s2)t2
-8.52m = -4.9m/s2 t2
-8.52m/-4.9m/s2 = t2
1.7s2 =t2
1.3 s = t

31. Practice problem y = ?? y = 35.0 m
Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height.
V2 - Vo2 = - 2g (y – yo)
Given:
vi = 26.2 m/s
vf = 0 m/s
a = –9.8 m/s2
y = ??
(0 m/s)2 = (26.2 m/s)2 + 2(-9.8m/s2)y
0 m2/s2 = m2/s2 + (-19.6 m/s2)y
0 m2/s m2/s2 =(-19.6 m/s2)y
m2/s2 =(-19.6 m/s2)y
y = ( m2/s2)/ (-19.6 m/s2)
y = 35.0 m

32. y-y.= v.t - ½ gt2 y= -420m g =9.8m/s2 -420m = 0.5 (9.8m/s2)t2
The observation deck of a skyscraper is 420 m above the street. Determine the time required for a penny to free-fall from the deck to the street below.
y= -420m
y-y.= v.t - ½ gt2
g =9.8m/s2
-420m = 0.5 (9.8m/s2)t2
-420m = -4.9m/s2t2
-420m/-4.9m/s2= t2
85.7m2/s2= t2
9.26s = t

33. Terminal Velocity
• An object that falls will experience a force due to gravity and a force due to the air.
• These forces are opposite in direction.
• The object will reach a point where the
forces balance, which means the object will no longer accelerate. It will continue with constant velocity.
• Terminal velocity is the point reached by an object where it will no longer accelerate.

34. A Ball Thrown Up Consider a ball that is thrown straight up.
• It will have maximum velocity the instant it
leaves your hand and when it returns to
your hand. (The ball is caught at the same
height.)
• On the way up, the ball will have negative
acceleration, therefore the ball’s velocity
will decrease.

35. Consider a rock thrown downward from a high altitude hot-air balloon
Consider a rock thrown downward from a high altitude hot-air balloon. If the initial velocity is 15 m/s and air resistance is neglected, what is the acceleration of the rock after one second?
What is the velocity of the rock?
9.8 m/s2