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Unit 1: Unit 1: Linear MotionLinear Motion
Sprayberry
Physics
2
Physics Comp BookUNIT 1: Linear Motion (@top, BIG!) p. 1
Copy GPS listed on the LTA. Circle the verbs; underline the nouns. Page Contents
2 Concept Map: Linear Motion pt. 1
3 linear motion, distance
4 displacement, speed
5 velocity, acceleration
6 Venn Diagram: Scalar vs. Vector
7 Concept Map: Linear Motion pt. 2
8 Lab SUMUPS:
* Distance vs. Displacement
* Froggy
3
Let’s do a Frayer model for linear motion:
Definition:
How to remember:
Drawing:
Motion in a straight line
linear motion
vertical horizontal
What it’s NOT:
4
Concept Map: Linear Motion p. 2
when an object moves we observe—
The position changing
How quickly the position changes
The rate at which the movement changes
called
called
called
called
called
which is
calculated by
which is
calculated by
which is
calculated by
which is
calculated by
which is
calculated by
5
When an object moves, we can observe:
The position changing Distance: how far it travels is called (in meters) Displacement: how far its position is from the starting point
(in meters with a direction) How quickly the position changes
Speed: how fast it’s covering distance
(or how much distance is covered in an amount of time) Velocity: how fast it’s position is moving and in what
direction relative to some other point (like home or a destination
The rate at which the movement changes Acceleration: is it speeding up or slowing down
For your concept map on p.2 of comp book!
6
Displacement Isn’t Distance The displacement of an object is not the same
as the distance it travels Example: Throw a ball straight up and then
catch it at the same point you released it The distance is twice the height The displacement is zero
7
Distance & Displacement
8
Distance & Displacement
B
A
C
5 m
4 m
3 m
Your distance traveled is 7m
You walk from A to B to C.What is your distance traveled?What is your displacement from A?
Your displacement form A is 5 m
9
Let’s do Frayers for distance & displacement in your comp book:
Definition:
Don’t confuse this with:How to remember:
How to calculate:
10
Instantaneous Speed is the speed at any specific instance or moment in time Ex. On a speedometer reading…
you are traveling 35 mph (mi/hr)
or 50 km/h or 25 m/s
Average Speed is the total distance covered divided by total time
Types of Speed
11
How do you calculate average speed?
The average speed of an object is defined as the total distance traveled divided by the total time elapsed
OR take the average:
(initial speed + final speed)
2 Speed is a scalar quantity
… why is it not a vector?
Average speed total distance
total time
Speed d
t
12
Speed, cont
Average speed totally ignores any variations in the object’s actual motion during the trip
The total distance and the total time are all that is important
SI units are m/s
13
Speed & Velocity Speed is the distance traveled in a certain
time.
Velocity is the displacement traveled in a certain time.
Velocity is speed in a given direction.
14
Velocity
The average velocity of an object is defined as the total displacement traveled divided by the total time elapsed
Velocity is a vector quantity
Average velocity total displacement
total timeV
x
t
15
Velocity
It takes time for an object to undergo a displacement
The average velocity is rate at which the displacement occurs
generally use a time interval, so let ti = 0
t
xx
tt
xx
t
xV if
if
ifaverage
16
Velocity, cont.
Direction will be the same as the direction of the displacement (time interval is always positive) + or - is sufficient to indicate direction
Units of velocity are m/s (SI), cm/s (cgs) or ft/s (US Cust.) Other units may be given in a problem, but
generally will need to be converted to these
17
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
18
Let’s do Frayers for speed & velocity in your comp book:
Definition:
Don’t confuse this with:How to remember:
How to calculate:
Wait for the next slide
19
Speed vs. Velocity
You drive from Yakima to Seattle (140 miles away) You stop in Ellensburg for a 2 hr lunch with a friend. Your total driving time is 2 hours What is the average speed? What is the average velocity?
(solve these questions in the Frayers)
(1) LIST (3) Equation
(2) LABEL w/units (4) Solve
Average speed 140 miles
2 hour 2 hour
Average speed 140 miles
4 hours35 mph
20
Constant Velocity
Constant velocity is constant velocity The instantaneous velocities are always the
same All the instantaneous velocities will also equal
the average velocity
21
Velocity Example 1
150 Km/hr
100 Km/hr
50 Km/hr
North
North
40º North of East
22
How fast is the plane moving in respect to the ground? 100 Km/hr
Wind35 Km/hr
Velocity Example 2
23
How fast is the plane moving in respect to the ground?
Notice the two velocities are occuring in the same LINE (linear motion…)
100 Km/hr
Wind35 Km/hr
Result
65 Km/hr
Velocity Example 2
24
Is this linear motion?
How fast is the plane moving in respect to the ground?
100 Km/hr
50 Km/hrWind
Velocity Example 3
25
How fast is the plane moving in respect to the ground?
100 Km/hr
50 Km/hrWind
Resultant
a2
b2c2
a2 b2 c2+ =
Velocity Example 3
26
How fast is the plane moving in respect to the ground?
100 Km/hr
50 Km/hrWind
Resultant
a2
b2c2
a2 b2 c2+ =
R2 = (100)2 + (50)2 R2 = 10,000 + 2500 R2 = 12,500R = 111.8 Km/hr
Velocity Example 3
27
Concept Map: Linear Motion p. 2
when an object moves we observe—
The position changing
How quickly the position changes
The rate at which the movement changes
called
called
called
called
called
which is
calculated by
which is
calculated by
which is
calculated by
which is
calculated by
which is
calculated by
Adding all the legs of the journey
distance
displacement
speed
velocity
acceleration
Xfinal –x initial
Total distanceTotal time
xfinal –x initial
time
vfinal –v initial
time
28
Scalar vs. Vector Scalar - magnitude only and units
(e.g. volume, mass, time, speed, distance)
magnitude means SIZE,
units: like meter, mile, etc.
Vector – magnitude, units & direction (e.g. weight, velocity, acceleration)
in other words:
where is this “thing” pointing?
29
Pictorial Representation
An arrow represents a vector Length = magnitude (size) of vector Direction = direction of vector
30
Pictorial Representation
This arrow could represent a vector of magnitude 10 point to the “right”
This arrow could represent a vector of magnitude 5 point to the “left”
31
Get your comp book…
Draw an empty Venn Diagram like this on p. 6
32
Label one side scalar, other vector
Magnitude Size Direction Units Distance Displacement Speed velocity Acceleration Mass Weight
12 cm 47 kg (mass) 470 Newtons (weight) 50 meters 50 meters West 25 m/s 25 m/s toward home 25 m/s away from home 10 m/s2
10 m/s2 toward the ground
Place these words in the correct space on the diagram:
33
Acceleration Change in velocity divided by the change in
time
a Vt
34
Acceleration
Great animation showing acceleration:http://www.physicsclassroom.com/mmedia/kinema/acceln.cfm
Changing velocity (not constant) means an
acceleration is present Acceleration is the rate of change of the velocity (how
fast the velocity changes)
Units: m/s2 (SI) other examples: cm/s2
ft/s2
35
Average Acceleration
Vector quantity When the sign of the velocity and the
acceleration are the same (either positive or negative), then the speed is increasing
When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing
36
Relationship Between Velocity & Acceleration
Uniform velocity (shown by red arrows maintaining the same size)
Acceleration equals zero
37
Relationship Between Velocity & Acceleration
Velocity and acceleration are in the same direction Acceleration is uniform (blue arrows maintain the
same length) Velocity is increasing (red arrows are getting longer) Positive velocity and positive acceleration
38
Relationship Between Velocity & Acceleration
Acceleration and velocity are in opposite directions Acceleration is uniform (blue arrows maintain the
same length) Velocity is decreasing (red arrows are getting shorter) Velocity is positive and acceleration is negative
39
Let’s do a Frayer for acceleration in your comp book:
Definition:
Don’t confuse this with:How to remember:
How to calculate:
Wait for the next slide
40
Acceleration Example 1
(solve this problem in the Frayer section…)
A car is moving at a speed of 35.8 m/s. If it takes 2.0 s to come to a complete stop, what acceleration would it have?
(1) LIST (3) Equation
(2) LABEL w/units (4) Solve
41
Acceleration Example 2
A car is said to go "zero to sixty in six point seven seconds". What is its acceleration in m/s2?
(1) LIST (3) Equation
(2) LABEL w/units (4) Solve
42
Acceleration Example 3
The driver from the previous problem can't release his foot from the gas pedal. (The gas pedal is also known as the accelerator. Coincidence? I think not.) How many additional seconds would it take for the driver to reach 80 mph? (assuming the acceleration hasn't changed)?
(1) LIST (3) Equation
(2) LABEL w/units (4) Solve