Braking Distance Lesson

Content Area: Physics (11-12)
Topic: Kinematics
Sub-Topic: Braking Distance

Computer requirements: Vensim, STELLATM or Excel
Prior content covered: Linear velocity and acceleration
Estimated time for computer portion of lesson: 60 min

Essential Questions or Ideas to address:

• How does the initial velocity affect braking distance?
• How does braking ability affect braking distance?
• For a given acceleration, what is the relationship between braking distance and initial velocity?

The lesson (90-min block):  Students use various resources to determine the braking abilities of one or models of cars.  The data given in car magazines is usually presented at distance to stop from 60 mph.  From this information and using the appropriate conversions, students calculate the braking accleration in ft/sec2.  They also create a table of velocities, converting 20, 30, 40, 50 and 60 mph to ft/s.  Then students build or use a model to look at the stopping distances for these other velocities.  A graph of stopping distance vs. initial velocity is developed and students are asked to determine if the relationship is linear.  If students have been assigned different vehicles with different braking accelerations to model, then students can also compare results between vehicles. An applet may be found at: http://www.mta.ca/faculty/science/physics/suren/Brake/Brake.html

• For a given acceleration, the relationship between initial velocity and braking distance is linear.

Evaluation of lesson effectiveness:  Students generally enjoy using car magazines to get data on vehicles.  They struggle with the unit conversions.  Use of the model is fairly simple and the graph produced is fairly clear to read and appears in math and physics textbooks.  There is value in relating the physics equations they are learning to real world applications.

Math topics: Linear and quadratic equations, graph interpretation for those equations, using a graph to determine a relationship, conversion of units

Extensions: Tailgate Lesson

Standards:

MSDE (from the website as of 9/05):

 Physics/Core Learning Goals Science Indicator 5.1.2 The student will use algebraic and geometric concepts to describe an object's motion. Assessment Limits direction, position, distance/displacement, speed/velocity, motion with a constant acceleration, one and two dimensional motion, frames of reference Goal 5 Concepts Of Physics The student will demonstrate the ability to use scientific skills and processes (Core Learning Goal 1) to explain and predict the outcome of certain interactions which occur between matter and energy. Expectation 5.1 The student will know and apply the laws of mechanics to explain the behavior of the physical world.

The standards do not directly address kinematics, but an understanding of motion is necessary before students can address the standards as they appear here.

National Science Standards:

Physical Science: Motion and Forces:
Objects change their motion only when a net force is applied. Laws of motion are used to calculate precisely the effects of forces on the motion of objects. The magnitude of the change in motion can be calculated using the relationship F = ma, which is independent of the nature of the force.  Whenever one object exerts a force on another, a force equal in magnitude and opposite in direction is exerted on the first object.

AAAS Benchmarks:

The Physical Setting: Forces of Nature:

• The change in motion of an object is is proportional to the applied force and inversely proportional to the mass.
• All motion is relative to whatever frame of reference is chosen, for there is no motionless frame from which to judge all motion.

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