linear motion chapter 2. motion everywhere – people, cars, stars, cells, electricity, electrons...

LINEAR MOTIONChapter 2

MotionEverywhere – people, cars, stars, cells, electricity, electronsRate = Quantity/time How fast something happens

Linear MotionMotion on a straight path Scalar- Distance and speed Vector – Displacement and velocity

Motion is RelativeEverything 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

SpeedsSnail - 2 meters/dayIndy racecar – 300 km/hrSpace shuttle – 8 km/sec

SpeedDistance / time “per” – divided by – “/”Any combination of units is useful depending on situation Km/hr, cm/day, light-years/hourMost common – m/sec and mile/hr

Average SpeedTotal distance/time intervalExamples: 60 km in 1 hour = 60 km/hr 240 km in 4 hour = 60 km/hr

Note the unitsDoes not indicate all the stops and starts

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

          The shorter the time period measured the closer it brings you to calculating an "instantaneous velocity".  Only if the time period

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

Constant SpeedIf the speed does not change over a long period, it is like Average speedLength = velocity x time l = vcont

Instantaneous SpeedSpeed at any moment Speed can vary with timeSpeedometer – measures instantaneous speed

The shorter the time period measured the closer it brings you to calculating an "instantaneous velocity".  Only if the time period becomes zero would we truly have an instantaneous velocity. 

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

Insert graph

Question 2

Chapter2Chapter Assessment Questions

A. 3 m

B. 8 m

C. 5 m

D. 5 cm

Chapter Assessment Questions

Answer: C

Answer 2

Chapter2

Reason: Distance d = df – di

Here, df = 8 m and di = 3 m

Therefore, d = 8 m 3 m = 5 m

QuestionsThe 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 speedAverage speed is the slope of the line during an intervalIf it is a curve, the instantaneous speed is the line tangent to the curve at that point

Delta NotationΔ – Greek capital letter – DeltaSignifies 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

VelocityEDL (every day life) – speed and velocity are interchangeablePhysics – 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 VelocityConstant speed and directionMust move in a straight line Curves change the directionChanging velocity- in a car there are 3 things to change velocity – Gas Brakes Steering wheel

The Displacement VectorDisplacement is the straight-line shift in position from Po to Pf Included length and directionVector Magnitude Direction

ResultantThe vector that is drawn between two points

Vector AlgebraRules for dealing with vectorsHelps us understand how to manipulate them

Tip-to-Tail MethodAdd 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 MethodOrder of addition is irrelevant

Parallelogram MethodUse 2 set vectors to make a parallelogram The diagonal is the resultant

Multiple VectorsAdd more than 2 vectors by the tip-to-tail method

Parallel VectorsParallel – Simple sum

Anti-parallel (opposite directions) - Difference

AccelerationHow fast is velocity changingAcceleration is a RATE (of a rate)Change in velocity Acceleration Deceleration Change in directionAcceleration = Change in velocity/time

QuestionSuppose 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 Accelerationa – acceleration

(m/s^2)v – velocity (m/s)t – time (s)

Average acceleration problemProblem – What is the acceleration

of a car the screeches to a stop from 96.54 km/h in 3.7 seconds?

Instantaneous AccelerationVelocity vs. Time graph Slope of line tangent is

equal to ACCELERATION

Sign of Slope Positive – accelerating Negative - decelerating

Velocity-Time Graph of Accelerating Car

TangentSlope = acceleration

velocity

time

Uniform accelerated motion

In the real world, acceleration is seldom constantIn problems, we can consider it constant for a few momentsMotion is in a straight line Vf – final velocity Vi – initial velocity

Uniform accelerated motion

vf = vi + atProblem – 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 SpeedWhat is vav for an object that is uniformly accelerating from vi to vf?

Mean speed = vav = ½ (vi + vf)

Area under the GraphEquals the total distance moved

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

More complexArea 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 + atvav = ½ (vi + vf)s = ½ (vi + vf) ts = vit + ½ at²vf² = vi² + 2as

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

When t is unknownProblem – 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 FastAn apple gains speed as it fallsGravity causes accelerationEDL – air resistance effects freefall acceleration

FreefallElapsed Time Instant. Speed (m/sec)

0 01 102 203 304 40t 10t

FreefallAcceleration = change in speedtime= 10 m/s/s = m/s2 Unit – meter/second/second

speed time intervalEquations : a = V instantaneous /t

V instantaneous = at

Gravity acceleration g = acceleration due to gravity Actually measures 9.81 m/s

2 In English – 32 ft/sec² Speedinstantaneous = acceleration x time

vinstantaneous = gt

QuestionWhat 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/s

2

Free Fall – How Far?Fast and far are differentAt the end of 1 sec the speed is 9.81m/s

2 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

QuestionDuring 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 gravityMathematical pattern for the distance something falls in time:

distance = ½ gravity x time2 d= ½ gt2

QuestionsAn 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 MotionVelocity vs. Time- freefall

Linear - directly proportionalSlope is constant = acceleration

Velocity

Time

Graphs of MotionDistance vs. Time

ParabolicSlope is variable = Speed

Distance

Time

Air resistanceEffects feathers and paperNot much effect on things with low profiles

How fast, far, and quicklyDon’t mix up fast and farAcceleration – rate of a rate Rate at which velocity changesBe patient – it took 2000 years from Aristotle to Galileo to straighten it all out!!