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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

- 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

- Things that seem at rest are moving in relation to stars and sun
- In this chapter – we look at motion compared to earth

Speeds

- Snail - 2 meters/day
- Indy racecar – 300 km/hr
- Space shuttle – 8 km/sec

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

- 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

The longer the time period measured, the more it leads to calculating an average velocity.

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 calculating an average velocity.

- Speed at any moment
- Speed can vary with time
- Speedometer – measures instantaneous speed

Chapter calculating an average velocity.

Chapter Assessment Questions2

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 calculating an average velocity.

2

Chapter Assessment QuestionsAnswer 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 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 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 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 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 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 calculating an average velocity.

- Displacement is the straight-line shift in position from Poto Pf
- Included length and direction

- Vector
- Magnitude
- Direction

Vector Algebra calculating an average velocity.

- Rules for dealing with vectors
- Helps us understand how to manipulate them

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

Parallelogram Method calculating an average velocity.

- Use 2 set vectors to make a parallelogram
- The diagonal is the resultant

Multiple Vectors calculating an average velocity.

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

Resultant

Resultant

Parallel Vectors calculating an average velocity.

- Parallel – Simple sum
- Anti-parallel (opposite directions) - Difference

Resultant

Resultant

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 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 calculating an average velocity.

a – acceleration (m/s^2)

v – velocity (m/s)

t – time (s)

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 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 calculating an average velocity.

Tangent

Slope = acceleration

velocity

time

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 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 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 calculating an average velocity.

- Equals the total distance moved
Area of a retangle = m/s x s = Meters

More complex calculating an average velocity.

- Area under still equals distance

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 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 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 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 calculating an average velocity.

- An apple gains speed as it falls
- Gravity causes acceleration
- EDL – air resistance effects freefall acceleration

Freefall calculating an average velocity.

Elapsed Time Instant. Speed (m/sec)

0 0

1 10

2 20

3 30

4 40

t 10t

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 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

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? 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? 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

- Did it travel 9.81 m?

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 calculating an average velocity.

- Mathematical pattern for the distance something falls in time:
distance = ½ gravity x time2

d= ½ gt2

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 calculating an average velocity.

- Velocity vs. Time- freefall
Linear - directly proportional

Slope is constant = acceleration

Velocity

Time

Graphs of Motion calculating an average velocity.

- Distance vs. Time
Parabolic

Slope is variable = Speed

Distance

Time

Air resistance calculating an average velocity.

- Effects feathers and paper
- Not much effect on things with low profiles

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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