# LINEAR MOTION - PowerPoint PPT Presentation

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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

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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

• 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

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

• Length = velocity x time

• l = vcont

### Instantaneous Speed

• Speed at any moment

• Speed can vary with time

• Speedometer – measures instantaneous speed

Chapter

### 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

2

### Chapter Assessment Questions

Reason:Distance d = df – di

Here, df = 8 m and di = 3 m

Therefore, d = 8 m  3 m = 5 m

### Questions

• 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

• 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

• 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

• 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 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

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

• Included length and direction

• Vector

• Magnitude

• Direction

### Resultant

• The vector that is drawn between two points

Resultant

### Vector Algebra

• Rules for dealing with vectors

• Helps us understand how to manipulate them

### Tip-to-Tail Method

• 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 Method

• Order of addition is irrelevant

B

A

A

B

B

A

### Parallelogram Method

• Use 2 set vectors to make a parallelogram

• The diagonal is the resultant

### Multiple Vectors

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

Resultant

Resultant

### Parallel Vectors

• Parallel – Simple sum

• Anti-parallel (opposite directions) - Difference

Resultant

Resultant

### Acceleration

• 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

• 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

a – acceleration (m/s^2)

v – velocity (m/s)

t – time (s)

### Average acceleration problem

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

### Instantaneous Acceleration

• 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

Tangent

Slope = acceleration

velocity

time

### Uniform accelerated motion

• 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

• 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

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

Mean speed = vav = ½ (vi + vf)

### Area under the Graph

• Equals the total distance moved

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

### More complex

• Area under still equals distance

### Mean Speed Theorem

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

• vf = vi + at

• vav = ½ (vi + vf)

• s = ½ (vi + vf) t

• s = vit + ½ at²

• vf² = vi² + 2as

### When vf 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

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

• An apple gains speed as it falls

• Gravity causes acceleration

• EDL – air resistance effects freefall acceleration

### Freefall

Elapsed Time Instant. Speed (m/sec)

00

110

220

330

440

t10t

### Freefall

• Acceleration = change in speed

time

= 10 m/s/s = m/s2

Unit – meter/second/second

speedtime interval

• Equations : a = V instantaneous /t

V instantaneous = at

### Gravity acceleration

• g = acceleration due to gravity

• Actually measures 9.81 m/s2

• In English – 32 ft/sec²

• Speedinstantaneous = acceleration x time

vinstantaneous = gt

### Question

• 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?

• On the way up it decelerates 9.81m/s2

• On the way down it accelerates 9.81m/s2

### Free Fall – How Far?

• 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

### Question

• 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

• Mathematical pattern for the distance something falls in time:

distance = ½ gravity x time2

d= ½ gt2

### Questions

• 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

• Velocity vs. Time- freefall

Linear - directly proportional

Slope is constant = acceleration

Velocity

Time

### Graphs of Motion

• Distance vs. Time

Parabolic

Slope is variable = Speed

Distance

Time

### Air resistance

• Effects feathers and paper

• Not much effect on things with low profiles

### How fast, far, and quickly

• 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!!