Modeling #4 - The Cab Control Problem

Slides:

Advertisements

Similar presentations

What is motion? An object is in motion when it’s distance from another object changes. What is a reference point? It is an object or place used to determine.

Advertisements

Acceleration Acceleration Velocity-time graph Questions.

T.H. The Professional Development Service for Teachers is funded by the Department of Education and Skills under the National Development Plan The Equations.

Linear Motion. Moving things have two different kinds of motion Linear Motion Harmonic Motion Motion is a change in position in a certain amount of time.

2.2 Acceleration Physics A.

Kinetic energy Derivation of kinetic energy. Kinetic Energy 2 starting equations F = m x a (Newton’s 2 nd law) W = Force x distance.

Kinematics Day 3. Kinematic Equations Used in situations with uniform acceleration.

Speed, Velocity and Acceleration What is speed? How is velocity different than speed? What is acceleration? Today’s Goal: Be able to use the proper equations.

Acceleration- Change in Velocity

Which line represents the greater speed? Graphing motion The greater the speed, the steeper the slope.

Acceleration- Change in Velocity occurs when an object _____________________ occurs when an object ______________ in speed. occurs when an object __________.

= constant speed forward = no speed, stopped = constant speed; negative direction Time (s) Distance mDistance m.

Relationship between time, displacement, velocity, acceleration. Kinematic.

Acceleration. The rate of change in velocity Acceleration The rate of change in velocity Examples…. –Speeding up Positive acceleration –Slowing down.

Velocity-time graphs. Edexcel Statements Velocity-time graph What story does the graph tell?

Velocity and Acceleration. Velocity Describes both speed and direction of an object. Describes both speed and direction of an object. How can an object.

1. What distance will a train stop in if its initial velocity is 23 m/s and its acceleration is m/s/s? 1058 m xvivfatxvivfat.

Acceleration Acceleration – the rate at which velocity changes  Can be an: Increase in speed Decrease in speed Change in direction.

Objectives Define speed and calculate speed from total time, total distance. Outcomes (5) Calculate speed and acceleration from practical observations.

Speeding Up and Slowing Down? Acceleration.

Acceleration. Acceleration – rate at which velocity changes Results from a change in speed and direction Acceleration = change in velocity = Δv timet.

Solving Word Problems Using Kinematics Equations.

Physics Support Materials Higher Mechanics and Properties of Matter b Solutions to Problems - Equations of Motion 27,27, 28, 33, 34, 35,28,33,34,35, Click.

1D Kinematics Equations and Problems. Velocity The rate at an object changes position relative to something stationary. X VT ÷ x ÷

Interpret The Graph. The graph shows an object which is not moving (at rest). The distance stays the same as time goes by because it is not moving.

Describing and Measuring Motion When is an object in motion? How do you know an object’s speed and velocity? How can you graph motion?

Distance, displacement, speed, velocity, solving equations

Velocity and Acceleration

This topic can be found in your textbook on pp

2-2 Acceleration At the start of a race what happens?

Today we will: Use different acceleration equations to solve for displacement, final velocity, initial velocity, and time. Begin review for test.

Cylindrical – Polar Coordinates

EQ: What is the difference between speed and velocity?

Speed can be calculated by Speed = Distance/Time

Modeling - The Cab Control Problem

Ch.5, Sec.1 – Measuring Motion

What is Motion?.

Jan 15 Question 1.

Lab 2.1 – Graphing one-dimensional Motion

Vectors and Calculus.

How to Describe & Recognize Motion

MOTION IN A STRAIGHT LINE GRAPHICALLY

Speed & Velocity.

Modeling #5 - The Cab Control Problem

Acceleration The rate at which velocity changes.

Modeling #5 - The Cab Control Problem

Modeling - The Cab Control Problem

Describing and Measuring Motion

Motion Section 1: Describing Motion Section 2: Velocity and Momentum

Modeling - The Cab Control Problem

Distance & Position Can you state the distance between the two cars? A

Modeling - The Cab Control Problem

The acceleration is the derivative of the velocity.

What is Motion? Motion: A change in position of an object compared to a reference point Motion can be measured in the following ways:

A car is decelerated to 20 m/s in 6 seconds

MOTION IN A STRAIGHT LINE GRAPHICALLY

Recognizing, Describing, and Measuring Motion

Velocity-time graphs In this section you will

#13 Speed and Momentum. #13 Speed and Momentum.

Baseline (Aiming for 4): List the factors

Calculate the distance in meters using the speed triangle

The Kinematics Equations

Distance & Position Can you state the distance between the two cars? A

Created for CVCA Physics By Dick Heckathorn 18 September2K+2

MOTION IN A STRAIGHT LINE GRAPHICALLY

Created for CVCA Physics By Dick Heckathorn 18 September2K+2

Recognizing, Describing, and Measuring Motion

Interpret The Graph.

Presentation transcript:

Modeling #4 - The Cab Control Problem The speed-of-approach algorithm employs:

Modeling - The Cab Control Problem Start as before with the equation for the velocity of the leading car A: Again use the numerical approach:

Modeling - The Cab Control Problem Then repeat for the trailing car B: 1. Calculate the acceleration an from the speed-of-approach algorithm 2. Calculate the velocity vn+1 3. Calculate the distance yn+1

Modeling - The Cab Control Problem 4. Calculate the relative speed: then compute the new acceleration from the speed of approach algorithm. 5. Increment the time, and repeat all of the calculations for both cab A and cab B

Modeling - The Cab Control Problem Note: Once again, you must limit the accelerations With “if” statements, or some other approach, you must stop the acceleration from exceeding the two limits (amax and -dmax)