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LINEAR MOTION. Chapter 2. Motion . Everywhere – people, cars, stars, cells, electricity, electrons Rate = Quantity/time How fast something happens. Linear Motion. Motion on a straight path Scalar- Distance and speed Vector – Displacement and velocity. Motion is Relative.

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Linear motion

LINEAR MOTION

Chapter 2


Motion
Motion

  • Everywhere – people, cars, stars, cells, electricity, electrons

  • Rate = Quantity/time

    • How fast something happens


Linear motion1
Linear Motion

  • Motion on a straight path

    • Scalar- Distance and speed

    • Vector – Displacement and velocity


Motion is relative
Motion is Relative

  • Everything moves

    • Things that seem at rest are moving in relation to stars and sun

      • Book on a desk moves at 30 km/sec in relation to the sun

      • Same book is even faster in the galaxy

  • In this chapter – we look at motion compared to earth


Speeds
Speeds

  • Snail - 2 meters/day

  • Indy racecar – 300 km/hr

  • Space shuttle – 8 km/sec


Speed
Speed

  • Distance / time

    • “per” – divided by – “/”

  • Any combination of units is useful depending on situation

    • Km/hr, cm/day, light-years/hour

  • Most common – m/sec and mile/hr


Average speed
Average Speed

  • Total distance/time interval

  • Examples:

    • 60 km in 1 hour = 60 km/hr

    • 240 km in 4 hour = 60 km/hr

      • Note the units

  • Does not indicate all the stops and starts



Constant speed
Constant Speed calculating an average velocity.

  • If the speed does not change over a long period, it is like Average speed

  • Length = velocity x time

  • l = vcont


Instantaneous speed
Instantaneous Speed calculating an average velocity.

  • Speed at any moment

  • Speed can vary with time

  • Speedometer – measures instantaneous speed


Chapter assessment questions

Chapter calculating an average velocity.

Chapter Assessment Questions

2

Question 2

Refer the adjoining figure and calculate the distance between the two signals?

  • Insert graph

  • 3 m

  • 8 m

  • 5 m

  • 5 cm


Chapter assessment questions1

Chapter calculating an average velocity.

2

Chapter Assessment Questions

Answer 2

Answer:C

Reason:Distance d = df – di

Here, df = 8 m and di = 3 m

Therefore, d = 8 m  3 m = 5 m


Questions
Questions calculating an average velocity.

  • The speedometer in every car also has an odometer that records distance:

    • If the odometer reads zero at the beginning of the trip and 35 km a half-hour later, what is the average speed?

    • Would it be possible to attain this average speed and never exceed 70 km/hr?

  • 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? In one minute?


Graph of constant speed
Graph of Constant speed calculating an average velocity.

  • Average speed is the slope of the line during an interval

  • If it is a curve, the instantaneous speed is the line tangent to the curve at that point


Delta notation
Delta Notation calculating an average velocity.

  • Δ – Greek capital letter – Delta

  • Signifies a change in a quantity

    Δl = l f – l i

    Δt = t f -t i

    v = Δl = l f – l i

    Δt t f - t i


Velocity
Velocity calculating an average velocity.

  • EDL (every day life) – speed and velocity are interchangeable

  • Physics – Velocity – speed in a direction

    • 60 km/hr North

  • Question – The speedometer of a car moving northward reads 60 km/hr. It passes another car that travels southward at 60 km/h. Do both cars have the same speed? Do they have the same velocity?


Constant velocity
Constant Velocity calculating an average velocity.

  • Constant speed and direction

  • Must move in a straight line

    • Curves change the direction

  • Changing velocity- in a car there are 3 things to change velocity –

    • Gas

    • Brakes

    • Steering wheel


The displacement vector
The Displacement Vector calculating an average velocity.

  • Displacement is the straight-line shift in position from Poto Pf

    • Included length and direction

  • Vector

    • Magnitude

    • Direction


Resultant
Resultant calculating an average velocity.

  • The vector that is drawn between two points

Resultant


Vector algebra
Vector Algebra calculating an average velocity.

  • Rules for dealing with vectors

  • Helps us understand how to manipulate them


Tip to tail method
Tip-to-Tail Method calculating an average velocity.

  • Add vectors by placing tip of one to the tail of the other.

    • The resultant is from the tail of one to the tip of another

A

B

B

A

Resultant


Tip to tail method1
Tip-to-Tail Method calculating an average velocity.

  • Order of addition is irrelevant

B

A

A

B

B

A


Parallelogram method
Parallelogram Method calculating an average velocity.

  • Use 2 set vectors to make a parallelogram

  • The diagonal is the resultant


Multiple vectors
Multiple Vectors calculating an average velocity.

  • Add more than 2 vectors by the tip-to-tail method

Resultant

Resultant


Parallel vectors
Parallel Vectors calculating an average velocity.

  • Parallel – Simple sum

  • Anti-parallel (opposite directions) - Difference

Resultant

Resultant


Acceleration
Acceleration calculating an average velocity.

  • How fast is velocity changing

  • Acceleration is a RATE (of a rate)

  • Change in velocity

    • Acceleration

    • Deceleration

    • Change in direction

  • Acceleration = Change in velocity/time


Question
Question calculating an average velocity.

  • Suppose a car moving in a straight line steadily increases its speed each second, first from 35 to 40 km/h, then from 40 to 45 km/h, then 45 to 50 km/h. What is its acceleration?

  • In 5 seconds a car moving in a straight line increases its speed from 50 km/h to 65 km/h, while a truck goes from rest to 15 km/h in a straight line. Which undergoes greater acceleration? What is the acceleration of each vehicle?


Average acceleration
Average Acceleration calculating an average velocity.

a – acceleration (m/s^2)

v – velocity (m/s)

t – time (s)


Average acceleration problem
Average acceleration problem calculating an average velocity.

Problem – What is the acceleration of a car the screeches to a stop from 96.54 km/h in 3.7 seconds?


Instantaneous acceleration
Instantaneous Acceleration calculating an average velocity.

  • Velocity vs. Time graph

    • Slope of line tangent is equal to ACCELERATION

    • Sign of Slope

      • Positive – accelerating

      • Negative - decelerating


Velocity time graph of accelerating car
Velocity-Time Graph of Accelerating Car calculating an average velocity.

Tangent

Slope = acceleration

velocity

time


Uniform accelerated motion
Uniform accelerated motion calculating an average velocity.

  • In the real world, acceleration is seldom constant

  • In problems, we can consider it constant for a few moments

  • Motion is in a straight line

    • Vf – final velocity

    • Vi – initial velocity


Uniform accelerated motion1
Uniform accelerated motion calculating an average velocity.

  • vf = vi + at

  • Problem – What is the final speed of a bicyclist moving at 25.0 km/h who accelerates +3.00 m/s^2 for 3.00 sec?


The mean speed
The Mean Speed calculating an average velocity.

  • What is vav for an object that is uniformly accelerating from vi to vf?

    Mean speed = vav = ½ (vi + vf)


Area under the graph
Area under the Graph calculating an average velocity.

  • Equals the total distance moved

    Area of a retangle = m/s x s = Meters


More complex
More complex calculating an average velocity.

  • Area under still equals distance


Mean speed theorem
Mean Speed Theorem calculating an average velocity.

s = ½ (vi + vf) t

Problem- A bullet is fired with a muzzle speed of 330m/s down a 15.2 cm barrel. How long does it take to travel down the barrel?


Constant acceleration equations the big five
Constant Acceleration Equations THE BIG FIVE calculating an average velocity.

  • vf = vi + at

  • vav = ½ (vi + vf)

  • s = ½ (vi + vf) t

  • s = vit + ½ at²

  • vf² = vi² + 2as


When v f is unknown
When v calculating an average velocity.f is unknown

  • One sports car can travel 100.0 ft in 3.30 seconds from 0m/s. What is the acceleration?


When t is unknown
When t is unknown calculating an average velocity.

Problem – What is the cheetah’s acceleration if it goes 0 to 72 km/hr in 2.0 seconds?

- How far will it go to be moving 17.9 m/s?


Freefall how fast
Freefall – How Fast calculating an average velocity.

  • An apple gains speed as it falls

  • Gravity causes acceleration

  • EDL – air resistance effects freefall acceleration


Freefall
Freefall calculating an average velocity.

Elapsed Time Instant. Speed (m/sec)

0 0

1 10

2 20

3 30

4 40

t 10t


Freefall1
Freefall calculating an average velocity.

  • Acceleration = change in speed

    time

    = 10 m/s/s = m/s2

    Unit – meter/second/second

    speed time interval

  • Equations : a = V instantaneous /t

    V instantaneous = at


Gravity acceleration
Gravity acceleration calculating an average velocity.

  • g = acceleration due to gravity

    • Actually measures 9.81 m/s2

    • In English – 32 ft/sec²

  • Speedinstantaneous = acceleration x time

    vinstantaneous = gt


Question1
Question calculating an average velocity.

  • What would the speedometer reading on the falling rock be 4.5 seconds after it drops from rest?

  • How about 8 seconds after it is dropped?

  • 15 seconds?


What about an object thrown upward
What about an object thrown upward? calculating an average velocity.

  • On the way up it decelerates 9.81m/s2

  • On the way down it accelerates 9.81m/s2


Free fall how far
Free Fall – How Far? calculating an average velocity.

  • Fast and far are different

  • At the end of 1 sec the speed is 9.81m/s2

    • Did it travel 9.81 m?

      • NO – it was accelerating from 0 m/s

    • 0 m/s  9.81 m/s

      • Average speed = 4.90 m/s


Question2
Question calculating an average velocity.

  • During the span of fall, the rock begins at 10 m/s and ends at 20 m/s. What is the average speed during this 1-second interval. What is its acceleration?


Distance in gravity
Distance in gravity calculating an average velocity.

  • Mathematical pattern for the distance something falls in time:

    distance = ½ gravity x time2

    d= ½ gt2


Questions1
Questions calculating an average velocity.

  • An apple falls from a tree and hits the ground in one second.

    • What is the speed upon striking the ground?

    • What is its average speed during the one second?

    • How high about ground was the apple when it first dropped?


Graphs of motion
Graphs of Motion calculating an average velocity.

  • Velocity vs. Time- freefall

    Linear - directly proportional

    Slope is constant = acceleration

Velocity

Time


Graphs of motion1
Graphs of Motion calculating an average velocity.

  • Distance vs. Time

    Parabolic

    Slope is variable = Speed

Distance

Time


Air resistance
Air resistance calculating an average velocity.

  • Effects feathers and paper

  • Not much effect on things with low profiles


How fast far and quickly
How fast, far, and quickly calculating an average velocity.

  • Don’t mix up fast and far

  • Acceleration – rate of a rate

    • Rate at which velocity changes

  • Be patient – it took 2000 years from Aristotle to Galileo to straighten it all out!!


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