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.

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Linear motion


Chapter 2



  • 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



  • Snail - 2 meters/day

  • Indy racecar – 300 km/hr

  • Space shuttle – 8 km/sec



  • 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

Linear motion

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

Constant speed

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

Instantaneous Speed

  • Speed at any moment

  • Speed can vary with time

  • Speedometer – measures instantaneous speed

Chapter assessment questions


Chapter Assessment Questions


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 Assessment Questions

Answer 2


Reason:Distance d = df – di

Here, df = 8 m and di = 3 m

Therefore, d = 8 m  3 m = 5 m



  • 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

  • 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

  • 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



  • 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

  • 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

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

    • Included length and direction

  • Vector

    • Magnitude

    • Direction



  • The vector that is drawn between two points


Vector algebra

Vector Algebra

  • Rules for dealing with vectors

  • Helps us understand how to manipulate them

Tip to tail method

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






Tip to tail method1

Tip-to-Tail Method

  • Order of addition is irrelevant







Parallelogram method

Parallelogram Method

  • Use 2 set vectors to make a parallelogram

  • The diagonal is the resultant

Multiple vectors

Multiple Vectors

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



Parallel vectors

Parallel Vectors

  • Parallel – Simple sum

  • Anti-parallel (opposite directions) - Difference





  • 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



  • 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

a – acceleration (m/s^2)

v – velocity (m/s)

t – time (s)

Average acceleration problem

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

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

Velocity-Time Graph of Accelerating Car


Slope = acceleration



Uniform accelerated motion

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 motion1

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

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

Area under the Graph

  • Equals the total distance moved

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

More complex

More complex

  • Area under still equals distance

Mean speed theorem

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

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 v f is unknown

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

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

Freefall – How Fast

  • An apple gains speed as it falls

  • Gravity causes acceleration

  • EDL – air resistance effects freefall acceleration



Elapsed Time Instant. Speed (m/sec)









  • Acceleration = change in speed


    = 10 m/s/s = m/s2

    Unit – meter/second/second

    speedtime interval

  • Equations : a = V instantaneous /t

    V instantaneous = at

Gravity acceleration

Gravity acceleration

  • g = acceleration due to gravity

    • Actually measures 9.81 m/s2

    • In English – 32 ft/sec²

  • Speedinstantaneous = acceleration x time

    vinstantaneous = gt



  • 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?

  • 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?

  • 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



  • 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

  • Mathematical pattern for the distance something falls in time:

    distance = ½ gravity x time2

    d= ½ gt2



  • 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

  • Velocity vs. Time- freefall

    Linear - directly proportional

    Slope is constant = acceleration



Graphs of motion1

Graphs of Motion

  • Distance vs. Time


    Slope is variable = Speed



Air resistance

Air resistance

  • Effects feathers and paper

  • Not much effect on things with low profiles

How fast far and quickly

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!!

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