Instantaneous Speed Science 1206.

Slides:

Advertisements

Similar presentations

A graph of the instantaneous velocity of an object over a specified period of time Time is independent (x-axis) Velocity is dependent (y-axis) Remember,

Advertisements

Warm Up Determine the anti-derivative. Then differentiate your answer to check your work Evaluate the definite integral: 3.

Unit 6 – Fundamentals of Calculus Section 6

Equation of a Tangent Line

Describing the graph of a Parabola

Find the slope of the tangent line to the graph of f at the point ( - 1, 10 ). f ( x ) = 6 - 4x

Miss Battaglia AB Calculus. Given a point, P, we want to define and calculate the slope of the line tangent to the graph at P. Definition of Tangent Line.

THE DERIVATIVE AND THE TANGENT LINE PROBLEM

Graphing motion. Displacement vs. time Displacement (m) time(s) Describe the motion of the object represented by this graph This object is at rest 2m.

Rates of Change and Tangent Lines Section 2.4. Average Rates of Change The average rate of change of a quantity over a period of time is the amount of.

Implicit Differentiation. Objectives Students will be able to Calculate derivative of function defined implicitly. Determine the slope of the tangent.

Difference between speed and velocity

Equations of Tangent Lines April 21 st & 22nd. Tangents to Curves.

Drawing Velocity Time Graphs from Position Time Graphs Uniform and Non-Uniform Motion.

Drawing Velocity Time Graphs from Position Time Graphs

Acceleration Section 5.3 Physics.

Uniform Motion. 1) Uniform (rectilinear) motion a) Constant Speed b) straight line c) same direction 2) Speed a) Distance covered in a period of time.

Speed vs. Time Graphs.

Physics Chapter 5. Position-Time Graph  Time is always on the x axis  The slope is speed or velocity Time (s) Position (m) Slope = Δ y Δ x.

Distance is the space between two points, commonly measured in metres (m). Distances between two points can depend on the path taken. Time (t) is the duration.

GOAL: USE DEFINITION OF DERIVATIVE TO FIND SLOPE, RATE OF CHANGE, INSTANTANEOUS VELOCITY AT A POINT. 3.1 Definition of Derivative.

Scalar- number and units Vector- number, unit and direction Position (x)- The location of an object Distance (d)- change in position without regard to.

Derivatives Limits of the form arise whenever we calculate a rate of change in any of the sciences or engineering, such as a rate of reaction in chemistry.

Physics Section 2.1 Describe motion in terms of frames of reference, displacement and graphs An object that changes its position is said to have a displacement.

READ PAGES Physics Homework. Terms used to describe Physical Quantities Scalar quantities are numbers without any direction Vector quantities that.

Constant, Average and Instantaneous Velocity Physics 11.

Motion Quiz. 1. The slope of a position (distance) vs time graph equals what quantity of the motion?

Section 1.4 The Tangent and Velocity Problems. WHAT IS A TANGENT LINE TO THE GRAPH OF A FUNCTION? A line l is said to be a tangent to a curve at a point.

Average and Instantaneous Velocity. Average or Instantaneous? Instantaneous velocity : the velocity of a moving object at one specific moment. Average.

Motion graphs pg.11. Create and interpret graphs of position versus time. Calculate velocity from the slope of the position vs. time graph. Create and.

Find Slope Given Two Points and an Equation. Objectives Find the slope of a line given two points. Find the slope of a line given an equation.

Graphs of a falling object And you. Objective 1: Graph a position –vs- time graph for an object falling from a tall building for 10 seconds Calculate.

Calculus Section 3.1 Calculate the derivative of a function using the limit definition Recall: The slope of a line is given by the formula m = y 2 – y.

Final Exam Review Chapters 3 & 4.

Graphical Interpretation of Motion in One Dimension

ST.JOSEPH'S HIGHER SECONDARY SCHOOL

Physics Section 2.1 Describe motion in terms of frames of reference, displacement and graphs A frame of reference is a system for specifying the precise.

Velocity and Speed Graphically

Accelerated Motion Chapter 3.

Speed and Velocity 11.2 Page

Speed and Velocity.

The Derivative and the Tangent Line Problems

Speed Key Question: Investigation 4A

Remember graphs are read from left to right like a book

THE DERIVATIVE AND THE TANGENT LINE PROBLEM

Points of intersection of linear graphs an quadratic graphs

Work on worksheet with 8 multiple choice questions.

Scientific Notation and Graphing

SCIENCE 1206 – MOTION Unit 3 Slideshow 3 - GRAPHS.

Graphing Review.

Graphs of Linear Motion

y=mx + b 4.3 Linear Equations Slope-Intercept Form y = 2x - 5

Instantaneous Speed Lesson 9 January 31st, 2011.

Today’s Target…. I can identify patterns and trends on a graph. Today I will identify patterns and trends on a graph showing the motion of an object.

Section 1 Displacement and Velocity

What Information Can We Take from Graphs?

Instantaneous Rates & Concept of Derivative

Welcome to AP Physics 1.

2.5 Writing Equations in Slope Intercept Form

Chapter 2 Uniformly Accelerated Motion

II. Describing Motion Graphing

Aim: How do we analyze position-time or Displacement-time graphs?

Distance Time Graphs.

Day 23 10/5/10 TOPIC: Converting an xt Graph to a vt Graph

Speed-Time Graphs Speed Time.

Speed-Time Graphs for Acceleration

Instantaneous Speed 10.7.

2.5 Basic Differentiation Properties

Presentation transcript:

Instantaneous Speed Science 1206

Instantaneous Speed (Vinst): Instantaneous Speed is the speed of an object at a particular moment in time. How do we determine instantaneous speed?

With Constant Speed Example: What is Vinst at 3.0 s? On the d-t graph, Vinst at 3.0 s = slope On a v-t graph, Vinst is found by interpolating back to the y-axis. In the case of CONSTANT SPEED, the slope at any point on the line is the same.

With Changing Speed Example: what is Vinst at 5.0 s? On the d-t graph, a CURVED LINE, we determine Vinst by getting the slope of the tangent to the point. On the v-t graph, Vinst is found by interpolating back to the y-axis.

What is a TANGENT? Tangent A straight line that touches a curve at only one specific point.

How do we draw tangents? Place your ruler on the curve at the specified point. Swivel ruler around until it is an equal distance from the curve on both sides of the point.

Draw tangent. Calculate the slope of the tangent.

HOMEWORK!!! Complete Worksheets 12, 13, 14 on pages 32-34 of your booklet!

Next stop  Unit 3 Test 1 Closed Book Test on Unit 3 Part 1Booklet Topics include: Significant Digits Scientific Notation Converting between Units Rearranging Equations Speed Calculations Distance-Time Graphs Instantaneous Speed Test Format: Multiple Choice Graph Questions TEST DATE :______________