chapter 2: linear motion kinematics. kinematics kinematics is the science of describing the motion...

Chapter 2: Linear MotionChapter 2: Linear Motion

KinematicsKinematics

KinematicsKinematics

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

• Kinematics is a branch of mechanics (SEM 1).

• The goal of any study of kinematics is to develop sophisticated models which serve to describe how real-world objects move.

Today’s ObjectivesToday’s 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

Measuring The Motion of ObjectsMeasuring The Motion of Objects

• Observe the lab table in the front of your class room. Is it in motion?

Think Again!

• Every time we describe the motion of an object, we must define 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 ReferenceFrame of Reference

Displacement• As an object moves from one location to

another, the length of a straight line path from the initial position to the final position is called the displacement.

Displacement (continued)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 reference frame!)

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.

Speed Speed • Speed is a measure of how fast something is going.

• We often talk about instantaneous speed (speed at any 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

VelocityVelocity• Velocity is a measure of how fast something is going

in a specified direction.

Average Velocity = Average Velocity = x / x / tt• Where xx is displacement

Review QuestionReview Question

During a race on level ground, Andra runs with an average velocity of 6.02 m/s to the east. What is Andra’s displacement after 137 s?

Holt Ch. 2 Pg. 44

SolutionSolution

Words you think mean the same thing...Words you think mean the same thing...• We often use the following words interchangeably:

Distance & displacementSpeed & velocity

• However, there is a Major Difference:

Displacement and velocity are vector quantities. That is, they have a magnitude and a direction.

32 mph North

6.29 m/s East18 Km South

LabLab

• Toy Car LabWith a focus on:– recording accurate data.– Repeatable trials– Careful interpretation of data

Day 2/3

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

Representing Motion With GraphsRepresenting 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 = YRun X

Displacement vs. Time

Day 4

Graphs (continued)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)

That’s Right!

Slope = Speed

In this case m = Y / X = Distance / time = speed!!!

Understanding SlopeUnderstanding Slope• Which car has a higher constant speed?

• Clearly the red car moves much faster then the blue car so it has a higher constant 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!!!!!

Understanding SlopeUnderstanding Slope

• What slope Is the biggest?• Which slope is equal to zero?• Which is slope is equal to one?

Slopes of CurvesSlopes of Curves• Can you define a constant slope for the graph

below?

• So explain what is happening to the speed in this graph.

Instantaneous SpeedInstantaneous Speed

• Speed at various times can still be found.• We must use slopes of ‘tangent’ lines.

Tangent LinesTangent 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.

Chapter 2 Problem 11 (Yes! It was Chapter 2 Problem 11 (Yes! It was Hard!) Hard!)

Problem solving strategies for difficult problems1.List Givens2.Draw a Picture3.Determine Equations that are Applicable4.Use algebra and THINK creatively to find a

solution