chapter 2, linear motion (sec. 1).ppt

8/12/2019 Chapter 2, Linear Motion (sec. 1).ppt

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Chapter 2: Linear Motion

Kinematics


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Kinematics

Kinematics is the science of describing themotion of objects using words, diagrams,numbers, graphs, and equations.

Kinematicsis a branch of mechanics (SEM 1).

The goalof any study of kinematicsis todevelop sophisticated models which serve todescribe howreal-world objects move.


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Todays Objectives

Understand what is meant by a reference

frame when describing motion.

Define and Explain the differences between

distance/displacement and speed/velocity.

Understand what a vector is and how it can be

used to represent a displacement or a velocity.

Day 1


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Measuring The Motion of Objects

Observe the lab table in the front of your class

room. Is it inmotion?

Think Again!


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Every time we describe the motion of an

object, we mustdefine a frame of reference.

A frame of reference consists of:

An origin (a starting point, like the point (0,0) on

a graph)

At least 1 Axis with consistent units.

And it is usually at rest (but not always!)

Frame of Reference


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Displacement

As an object moves from one location toanother, the length of a straight line path from

the initial position to the final position is

called the displacement.


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Displacement (continued)

Displacement is not always equal to distance

traveled.

Observe your teacher take 2 steps forward then 2

steps back!

Displacement can be positive or negative.

(Remember, we measure from a referenceframe!)


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Your Turn!

3 km

3 km

1.5

km

1.5

km

1. What is the total distance traveled in meters?

= 1.5 + 3 + 3 + 1.5 = 9 km = 9x103

m = 9,000 m

2. What is the total displacement in meters?

= 0 m

A long distance runner travels the path shown.


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Speed

Speed is a measure of how fast something is going.

We often talk about instantaneous speed (speed atany instant, like what your speedometer on your car

reads) and measured average speed (the total distance

traveled divided by the total time it takes).

Average Speed = distance / time

Example Units: Mph Km/hr m/s


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Velocity

Velocityis a measure of how fast something is goingin a specified direction.

Average Velocity = x / t Where xis displacement


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Review Question

During a race on level ground, Andra runs with

an average velocity of 6.02 m/s to the east.

What is Andras displacement after 137 s?

Holt Ch. 2 Pg. 44


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Solution


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Words you think mean the same thing...

We often use the following words interchangeably:

Distance & displacement

Speed & velocity

However, there is a MajorDifference:

Displacement and velocity are vector quantities.

That is, they have a magnitude and a direction.

32 mph North

6.29 m/s East

18 Km South


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Lab

Toy Car Lab

With a focus on:

recording accurate data.

Repeatable trials

Careful interpretation of data

Day 2/3


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So far, We have discussed several ways to represent velocityand speed: words, numbers, equations, and now graphs.

Representing Motion With Graphs

Position = Distance (in cm for lab)

Note that your line points up and to the

right. This is considered a positive slope.

Remember m = slope = Rise = DY

Run DX

Displacement vs. Time

Day 4


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Graphs (continued)

Speed = distance / time

in this lab:

S = x / t

Recall: m = Slope = Rise/Run

= Y / x

Using the Information given, what does the slope represent in this following

graph? (see question # 15 on your lab as well)

Thats Right!

Slope = Speed

In this case m = Y / X =

Distance / time = speed!!!


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Understanding Slope

Which car has a higher constant speed?

Clearly the red car moves much faster then the blue car so it has a higherconstant speed.

But also look at the graphs! The slope of the red line is steeper than the blue

line.

Rule: A steeper line means bigger slope.

In this case, the bigger slope is the bigger constant speed!!!!!


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Understanding Slope

What slope Is the biggest?

Which slope is equal to zero?

Which is slope is equal to one?


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Slopes of Curves

Can you define a constant slope for the graphbelow?

So explain what is happening to the speed in thisgraph.


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Instantaneous Speed

Speed at various times can still be found.

We must use slopes of tangent lines.


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Tangent Lines

Do not cross (intersect) the curve.

Touch the curve at only one point.

Indicate the instantaneous speed for any point

on a distance vs. time graph.


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Chapter 2 Problem 11 (Yes! It was

Hard!)

Problem solving strategies for difficult problems

1. List Givens

2. Draw a Picture3. Determine Equations that are Applicable

4. Use algebra and THINK creatively to find a

solution

chapter 2, linear motion (sec. 1).ppt

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