1. UNIT 2A
Linear Motion

2. distance | speed | direction acceleration
Unit 2A: Linear Motion
(Chap 2)
You can describe the motion of an object by its:
distance | speed | direction acceleration

3. How do you know if an object is moving? Is your book moving?
2.1 Motion Is Relative
How do you know if an object is moving?
Is your book moving?
The book is at rest,
relative to the table, BUT
It’s moving at about
30 km/s relative to the sun.
An object is moving if its position relative to a fixed point is changing.

4. An object’s motion must be described relative to something else.
2.1 Motion Is Relative
An object’s motion must be described relative to something else.
shuttle 8 km/s relative to Earth below
race car 300 km/h relative to the track
The speeds of things on Earth are usually measured relative to the Earth’s surface.

5. Problem:
You are a passenger in a car stopped at a stop sign. Out of the corner of your eye, you notice a tree on the side of the road begin to move forward.
WHAT??
You have set yourself as the reference point as the car rolls slightly backward.
Reference point
Motion

6. 2.2 Speed
400 yrs ago, people described motion as simply “slow” or “fast.”
Galileo was the first to measure speed by the distance covered and the time it takes.
5 mi
0.20 h
distance
time
avg. speed =
speed =
avg. speed =
25 mi/h

7. 2.2 Speed

8. Instantaneous Speed Cars do not always move at a constant speed.
You can tell the speed of the car at any instant by looking at the car’s speedometer.
instantaneous speed:
the speed at any instant
average speed:
total distance
time

9. 320 km distance speed = time distance = 80 km = x km 1 h 4 hr
If we know average speed and travel time, the distance traveled is easy to find.
Example: If your average speed is 80 km/h on a 4-hour trip, then how far did you travel?
distance = 80 km = x km
1 h hr
distance
time
speed =
distance = speed x time
320 km

10. 2.2 Speed
If a cheetah can maintain a constant speed of 25 m/s, it will cover 25 meters every second.
At this rate, how far will it travel in 10 seconds?
distance = (25 m) = (x m) =
(1 s) 10 s
In 1 minute?
distance = (25 m) x (x m) =
(1 s) (60 s)
250 m
distance = speed x time
1500 m

11. distance time 35 km 0.5 h speed = = =
The speedometer in every car also has an odometer that records the distance traveled. If the odometer reads zero at the beginning of a trip and 35 km a half hour later,
what is the average speed?
distance
time
35 km
0.5 h
speed = = =
70 km/h

12. Quick Quiz!
Jake walks east through a passenger car on a train that moves 10 m/s in the same direction. Jake’s speed relative to the car is 2 m/s. Jake’s speed relative to an observer at rest outside the train is ___.
2 m/s
5 m/s
8 m/s
12 m/s
2.1

13. Quick Quiz.
A gazelle travels 2 km in a half hour. The gazelle’s average speed is ___.
1/2 km/h
1 km/h
2 km/h
4 km/h
2.2

14. ∆d t m s v = (m/s) In physics, Velocity: is speed in a direction.
speed: 60 km/h
velocity: 60 km/h north, or right, or down…
∆: change in…
(final – initial)
(df – di) t ∆d t m s
v =
(m/s)

15. If either the speed or the direction (or both)
2.3 Velocity
If either the speed or the direction (or both)
changes, then the velocity changes.
constant speed and constant velocity are NOT the same.
The car speedometer always reads 30 km/h.
Is speed constant?
Is velocity constant? Y N

16. ∆v a = t We can change an object’s motion by changing
2.4 Acceleration
We can change an object’s motion by changing
its speed, its direction, or both.
Acceleration is the rate at which velocity changes. ∆v t
(vf – vi) t
a =
acceleration can increase or decrease speed,

17. 2.4 Acceleration
We can change an object’s motion by changing its speed, its direction, or both.
Acceleration: is the rate at which velocity changes. ∆v t
(vf – vi) t
a =
acceleration can increase or decrease speed,
deceleration is really negative acceleration (–a)

18. 2.4 Acceleration
Acceleration concerns change in velocity so any a change in direction is acceleration.
The car speedometer always reads 30 km/h.
Is velocity constant?
Is there an acceleration? N Y

19. a in the same direction as v : speed up
2.4 Acceleration
a in the same direction as v : speed up

20. a in the same direction as v : speed up
2.4 Acceleration
a in the same direction as v : speed up
a in the opp. direction as v : slow down

21. a in the same direction as v : speed up
2.4 Acceleration
a in the same direction as v : speed up
a in the opp. direction as v : slow down
a at an angle to v : change direction

22. ∆v t m/s s m s2 a = or 10 m/s – 0 m/s 1 s 10 m/s 1 s a = = =
2.4 Acceleration
v units are in distance per time: (m/s)
a is the change in v per change in time.
a units are v per time: (m/s per s) or (m/s2)
changing v from 0 m/s to 10 m/s in 1 s,
a is… ∆v t
m/s s m s2
a = or
10 m/s – 0 m/s
1 s
10 m/s
1 s
a = = =
10 m/s2

23. 2.4 Acceleration
In 5 seconds a car increases its speed from 8 m/s to 18 m/s, while a truck goes from rest to 10 m/s in a straight line. Which undergoes greater acceleration?
18 m/s – 8 m/s
5 s
10 m/s
5 s
acar = = =
2 m/s2
10 m/s – 0 m/s
5 s
10 m/s
5 s
atruck = = =
2 m/s2

24. Constant speed in a constant direction is… constant velocity.
Quick Quiz!
Constant speed in a constant direction is…
constant velocity.
constant acceleration.
instantaneous speed.
average velocity.
2.3

25. A vehicle undergoes acceleration when it __. gains speed.
Quick Quiz.
A vehicle undergoes acceleration when it __.
gains speed.
decreases speed.
changes direction.
ALL of the above
2.4

26. During each 1 s of fall, v increases by 10 m/s. This gain in v in m/s
2.5 Free Fall: How Fast
Imagine there is no air resistance and that gravity is the only thing affecting a falling object.
An object moving under influence of the gravitational force only is said to be in free fall.
During each 1 s of fall, v increases by 10 m/s.
This gain in v in m/s
is a in m/s2.

27. g = –10 m/s2 v = vi + at g is used for the acceleration due to gravity
2.5 Free Fall: How Fast
t = 0 s, v = 0 m/s
g is used for the acceleration due to gravity
Although g varies slightly based on altitude, its average value is nearly 10 m/s2
t = 1 s, v = 10 m/s
t = 2 s, v = 20 m/s
t = 3 s, v = 30 m/s
t = 4 s, v = 40 m/s
g = –10 m/s2
v = vi + at
(a is g)
t = 5 s, v = 50 m/s

28. An object is thrown straight up: It moves upward for a while.
2.5 Free Fall: How Fast
An object is thrown straight up:
It moves upward for a while.
What is v at its highest point?
Going up, vi goes to 0 m/s.
a = ?
It then falls downward as if it had been dropped from rest,
going from 0 m/s back to vi (but downward)
v = 0 m/s at hmax vo
a = –10 m/s2
= g
a = –10 m/s2
= g

29. 2.5 Free Fall: How Fast
What would the speedometer reading on the falling rock be 4.5 seconds after it drops from rest? (v = ?)
v = vi + at
v = 0 m/s + (–10 m/s2)(4.5 s)
(a is g)
v = –45.0 m/s
How about 8 seconds after it is thrown with an initial velocity of 20 m/s downward?
v = –20 m/s + (–10 m/s2)(8 s)
v = –100 m/s

30. With what objects might air resistance be small enough to be ignored?
2.8 Air Resistance and Falling Objects
Drop a feather and a coin and the coin reaches the floor far ahead of the feather. Why?
Air resistance is responsible for these different accelerations. (not just g)
In a vacuum, the feather and coin fall with exactly the same acceleration, g.
With what objects might air resistance be small enough to be ignored?

31. g = –10 m/s2 v = vi + at d = vit + ½at2 2.6 Free Fall: How Far
t = 0 s, v = 0 m/s, d = 0 m
t = 1 s, v = 10 m/s, d = 5 m
t = 2 s, v = 20 m/s, d = 20 m
g = –10 m/s2
t = 3 s, v = 30 m/s, d = 45 m
vavg = ( ) 2
vavg = 35 m/s
1 s
d = 35 m
v = vi + at
(a is g)
t = 4 s, v = 40 m/s, d = 80 m
d = vit + ½at2
vavg = ( ) 2
vavg = 45 m/s
d = 45 m
1 s
t = 5 s, v = 50 m/s, d = 125 m

32. vf = vi + at An apple falls to the ground in 3 s.
2.6 Free Fall: How Far
An apple falls to the ground in 3 s.
What is its speed upon striking the ground?
vf = vi + at
(a is g)
v = 0 m/s + (10 m/s2)(3 s)
v = 30 m/s
What is its vavg during the 3 s?
1 s
vavg = (vf + vi) 2
vavg = 15 m/s
2 s
vavg = (0 m/s + 30 m/s) 2
3 s

33. d = vit + ½at2 An apple falls to the ground in 3 s.
2.6 Free Fall: How Far
An apple falls to the ground in 3 s.
How high above ground was the apple when it first dropped?
v = 30 m/s
vavg = 15 m/s
d = vit + ½at2
(a is g)
1 s
d = (0 m/s)(3 s) + ½(10 m/s2)(3 s)2
2 s
d = 45 m
3 s

34. Linear Motion - Practice Problems
1) An angry mob lynches a physics teacher after receiving their grades. They throw the
physics teacher off a tall building straight down with a velocity of 20 m/s. The teacher falls for 3.0 seconds landing on a stack cardboard boxes. From what height was he thrown?
d = vi t + ½ at2

35. Linear Motion - Practice Problems
2) Find the uniform acceleration that causes a car’s velocity to change from 32m/s to 96m/s in an 8.0s period.
3) A car with a velocity of 22m/s is accelerated uniformly at a rate of 1.6m/s for 6.8s. What is the final velocity?
vf = vi + at
vf = vi + at

36. Linear Motion - Practice Problems
4) An airplane starts from rest and accelerates at a constant 3.0m/s2 for 30s before leaving the ground.
How far did it move?
How fast was it going at liftoff?
d = vi t + ½ at2
vf = vi + at

37. Linear Motion - Practice Problems
5) Your sister drops your house keys down to you from the second floor window. If you catch them 4.3 m from where your sister dropped them, what is the velocity of the keys when you catch them?
d = vit + 1/2at

40. gravity doesn’t act in a vacuum.
Quick Quiz!
In a vacuum tube, a feather is seen to fall as fast as a coin. This is because …
gravity doesn’t act in a vacuum.
air resistance doesn’t act in a vacuum.
greater air resistance acts on the coin.
gravity is greater in a vacuum.
2.8

41. Quick Quiz.
If a falling object gains 10 m/s each second it falls, its acceleration can be expressed as _________.
10 m/s/s
10 m/s2
v = gt
both A and B
2.5

42. d = vit + ½at2
Quick Quiz.
A rock falls 180 m from a cliff into the ocean. How long is it in free fall?
6 s
10 s
18 s
180 s
180 = (0)t + ½(10)t2
180 = ½(10)t2
180 = 5t2
180 = t2 5
36 = t2
√36 = t
t = 6 s
2.6

43. Graphs can visually describe relationships.
2.7 Graphs of Motion
Equations, tables, and pictures are not the only way to describe relationships between distance, velocity, and acceleration.
Graphs can visually describe relationships.

44. constant velocity (a = 0)
2.7 Graphs of Motion
distance vs. time:
constant velocity (a = 0)
slope = distance = v
time
distance (m)
time (s)

45. constant acceleration (+a)
2.7 Graphs of Motion
distance vs. time:
constant acceleration (+a)
slope = distance = v
time
parabolic curve b/c time is squared
(quadratic)
d = ½at2
distance (m)
time (s)

46. distance vs. time → + → + ← – ← –
2.7 Graphs of Motion
distance vs. time 1 2
dir:v :
a : → +
fast
dir:v :
a : → +
slow d d t t 3 4
dir:v :
a :
dir:v :
a : ← –
fast ← –
slow d d t t

47. distance (m) time (s) Describe the motion. v : 0 a : 0 v : + a : 0
2.7 Graphs of Motion
v : 0
a : 0
v : +
a : 0
distance (m)
time (s)
moves forward at v = 5 m/s for 5 s.
stops at 25 m (v = 0 m/s) for 5 s.

48. velocity (m/s) time (s)
2.7 Graphs of Motion
velocity vs. time: constant velocity (a = 0)
slope = velocity = a
time
velocity (m/s)
time (s)

49. velocity (m/s) time (s)
2.7 Graphs of Motion
velocity vs. time: constant acceleration (+a)
velocity (m/s)
slope = velocity = a
time
time (s)

50. dir: v : a : right + (constant) dir: v : a : left – (constant) dir:
2.7 Graphs of Motion
dir:
v :
a :
right
+ (constant)
dir:
v :
a :
left
– (constant)
dir:
v :
a :
right
+ (faster) +
dir:
v :
a :
right
+ (slower) –
dir:
v :
a :
left
– (slower) +
dir:
v :
a :
left
– (faster) –

51. 2.7 Graphs of Motion
Consider the graph below. Describe the motion.
(include all that are true):
moving forward
constant velocity
positive velocity
negative velocity
slowing down
changing directions
speeding up
positive acceleration
constant acceleration
negative acceleration + v t –

52. The slope of a velocity-versus-time graph represents ____. distance
Quick Quiz!
The slope of a velocity-versus-time graph represents ____.
distance
velocity
acceleration
time

53. A. t = 0-1 s B. t = 1-4 s C. t = 4-9 s D. t = 9-12 s
WARM UP
Consider the graph below. Describe the motion from...
A. t = 0-1 s B. t = 1-4 s C. t = 4-9 s D. t = 9-12 s
v =
a =
→, faster +
v =
a =
→, faster +
v =
a =
→, slower + –
v =
a =
←, faster –
At what time
is v = 0 m/s
v = 0 m/s at 9 s

54. Equations Summary distance time speed = ∆d t vavg = (vf + vi) 2 v =
NOT
given on test
distance
time N
speed = N
given on test ∆d t
vavg = (vf + vi) 2
v =
v = vi + at ∆v t
a =
d = vit + ½at2
g = –10 m/s2

55. WS Motion Graphs
Begin your worksheet now.
We will take all of class tomorrow to finish it.

56. distance vs. time dir:v : __ dir:v : __ a : a : dir:v : __ dir:v : __
2.7 Graphs of Motion
distance vs. time 1
dir:v :
a : __
_____ 2
dir:v :
a : __
____ d d t t
dir:v :
a : 3 __
_____ 4
dir:v :
a : __
_____ d d t t

57. velocity vs. time dir: v : a : _____ __ (______) __ dir: v : a : _____
2.7 Graphs of Motion
velocity vs. time
dir:
v :
a :
_____
__ (______) __
dir:
v :
a :
_____
__ (______) __
dir:
v :
a :
_____
__ (______) __
dir:
v :
a :
_____
__ (______) __
dir:
v :
a :
_____
__ (______) __
dir:
v :
a :
_____
__ (______) __

58. Acceleration & Velocity Graphs
VIDEO – Part 1
(7:19)
Acceleration & Velocity Graphs

59. Acceleration & Velocity Graphs
VIDEO – Part 2
(9:53)
Acceleration & Velocity Graphs

60. Acceleration & Velocity Graphs
VIDEO – Part 3
(7:45)
Acceleration & Velocity Graphs