Texas Instruments CBR 2 manual Mathematics of distance, velocity, and acceleration

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Teacher Information (cont.)

A typical CBR 2™ motion detector Velocity-Time plot actually represents speed, not velocity. Only the magnitude (which can be positive, negative, or zero) is given. Direction is only implied. A positive velocity value indicates movement away from the CBR 2™ motion detector; a negative value indicates movement toward the CBR 2™ motion detector.

The CBR 2™ motion detector measures distance only along a line from the detector. Thus, if an object is moving at an angle to the line, it only computes the component of velocity parallel to this line. For example, an object moving perpendicular to the line from the CBR 2™ motion detector shows zero velocity.

The mathematics of distance, velocity, and acceleration

d2

 

d1

Distance-Time plot

t1 t2

Vaverage =

@d

=

d2

N d1

= slope of Distance-Time plot

@t

t2

N t1

 

 

 

 

Vinstantaneous = @limt"0(@@dt ) = d(s)dt

where s = distance

v1

 

 

 

 

 

 

v2

 

 

 

 

 

Velocity-Time plot

 

t1

t2

 

 

Aaverage =

@v

=

v2

N v1

= slope of Velocity-Time plot

@t

t2

N t1

 

 

 

lim (@v) dv

Ainstantaneous = @t"0 @t = dt

34 GETTING STARTED WITH THE CBR 2™ SONIC MOTION DETECTOR

© 1997, 2004, 2006 TEXAS INSTRUMENTS INCORPORATED

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Contents Getting Started with the CBR 2 Sonic Motion Detector Important notice regarding book materials Table of Contents What is the CBR 2 Sonic Motion Detector? What does the CBR 2 sonic motion detector do?What’s in this guide? With a range between Download Getting started with the CBR 2 Sonic Motion DetectorRun Important informationHints for effective data collection Getting better samplesClear zone Sample Interval Speed of sound Activity 1-Graphing Your Motion Notes for Teachers Activity 1-Graphing Your Motion Linear ObjectivesData collection Distance vs. Time Graphs TI-83/84 Family users TI-89/Titanium/92+/V200 Activity 1-Graphing Your Motion Linear Activity 2-Match the Graph Typical plotTypical answers Activity 2-Match the Graph Linear Data collectionExplorations Study the graph and answer questions 13, 14,Activity 2-Match the Graph Name Activity 3-A Speedy Slide Sample resultsExtensions Activity 3-A Speedy Slide Parabolic Data collection, Part 1, Sliding SpeedActivity 3-A Speedy Slide Parabolic Activity 3-A Speedy Slide Parabolic Data collection, Part 2, a Speedier Slide Speedier Slide Plan DataData processing Activity 3-A Speedy Slide Activity 4-Bouncing Ball ExplorationsAdvanced explorations Activity 4-Bouncing Ball Parabolic Advanced explorations Distance-Time plot of the bounce forms a parabolaActivity 4-Bouncing Ball How do the data plot and the Yn graph compare?Activity 5-Rolling Ball Activity 5-Rolling Ball Parabolic Answer question Activity 5-Rolling Ball Teacher Information L3n = Mathematics of distance, velocity, and acceleration = slope of Distance-Time plotWeb-site resources Additional resourcesUsing the data lists Sonic motion detector data is stored in listsCollected data is stored in lists L1, L2, L3, L4 in Ranger EasyData Settings TI-83 and TI-84 Family Calculators Changing EasyData settingsRestoring EasyData settings to the defaults TI83/84 Family TI89/Titanium/92+/V200 1997, 2004, 2006 Texas Instruments Incorporated Batteries If you have this problem Try this Case of difficultyEasyData Menu Map TI-83 and TI-84 Family Calculators Ball Bounce InstructionsTI Service and Warranty Texas Instruments TI Warranty InformationFor US Customers Only Customers in the U.S. and Canada OnlyFCC information concerning radio frequency interference Australia & New Zealand Customers onlyAll Other Customers

CBR 2 specifications

Texas Instruments has long been a prominent player in the field of educational technology, and the CBR 2 (Calculator-Based Ranger 2) is a testament to their commitment to enhancing the learning experience, particularly in the realms of mathematics and science. Designed to complement graphing calculators, the CBR 2 is a versatile data-collection device that empowers students and educators to explore real-world phenomena through hands-on experimentation.

One of the main features of the CBR 2 is its ability to capture a wide array of data through various sensors. The device is equipped with an array of built-in sensors that can measure motion, including speed and distance. This makes it an invaluable tool for physics experiments, allowing students to visualize concepts such as speed, acceleration, and trajectory.

The CBR 2 utilizes ultrasonic technology to detect distance through sound waves. This feature enables students to conduct experiments that demonstrate principles of sound and motion in a tangible way. With a range of up to 6 meters, the CBR 2 provides accurate and reliable measurements that can be graphically represented using compatible Texas Instruments graphing calculators.

The device is highly user-friendly, with simple interfaces that allow users to easily collect and analyze data. The integration with graphing calculators simplifies the process of data visualization, enabling students to create graphs in real time as they conduct experiments. This capability is particularly beneficial in encouraging interactive learning and fostering a deeper understanding of scientific principles.

The CBR 2 is designed to be portable and durable, making it suitable for classroom settings as well as outdoor experiments. Its compact size and lightweight construction ensure that it can be easily transported, allowing educators to take learning beyond the confines of the classroom.

The CBR 2 also supports various modes of data collection, including Event Mode, which allows users to trigger data collection based on specific events. This feature is useful in demonstrating concepts such as projectile motion and collisions, providing students with hands-on experience that enhances their learning.

In summary, Texas Instruments' CBR 2 is a powerful educational tool that enables students to collect, analyze, and visualize data in an engaging manner. With its built-in sensors, ultrasonic technology, and seamless integration with graphing calculators, the CBR 2 stands out as a versatile device that enriches the educational experience. It not only provides a platform for conducting experiments but also cultivates critical thinking skills and a deeper understanding of scientific concepts, preparing students for a future in STEM fields.
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