Unit 3 Objectives

Alignment with KY Program of Studies:     Constant Acceleration

Problem Solving Suggestions

You should be able to determine the instantaneous velocity of an object three ways

• find the slope of the tangent to a x vs. t graph at a given point

• use the mathematical model v_f = v_o+ at

• use the mathematical model v_f ² = v_o ² + 2aDx 

• You should be able to determine the displacement of an object three ways

  • find the area under a v vs. t curve

  • use the mathematical model Dx = v_ot + (1/2)at²

  • use the mathematical model v_f² = v_o² + 2aDx

•  You should be able to determine the acceleration of an object five ways:

  • find the slope of a v vs. t graph

  • use the mathematical model a = Dv/Dt

  • use the mathematical model Dx = v_ot + (1/2)at²

  • use the mathematical model v_f = v_o+ at

  • use the mathematical model v_f² = v_o² + 2aDx

• Given a x vs. t graph, you should be able to:

  • describe the motion of the object (starting position, direction of motion, velocity)

  • draw the corresponding v vs. t graph

  • draw the corresponding a vs. t graph

  • determine the instantaneous velocity of the object at a given time

• Given a v vs. t graph, you should be able to:

  • describe the motion of the object (direction of motion, acceleration)

  • draw the corresponding x vs. t graph

  • draw the corresponding a vs. t graph

  • write a mathematical model to describe the motion

  • determine the acceleration

  •  determine the displacement for a given time interval

• You should be able to solve complex acceleration problems 

  • Example- speeder and patrolman problem (graph x vs t - find the intersection of the lines.  You should know how to find the intersection of 2 graphs using your calculator- for a tutorial see the Appendix)

  • Example- car catching train problem ( graph velocity vs time - generate equations using the slope of the line and the area under the curve.  You will have 2 equations and 2 unknowns-- recall from Algebra how to solve a system of equations.  If you need to solve a quadratic equation you may use the SOLVER on your calculator, or solve for zeroes using your calculator.  See the Appendix for calculator tutorial)

  Kentucky Core Content:

  Laws of motion. Objects change their motion only when a net force is applied. Laws of motion are used to predict and/or calculate the effects of forces on the motion of objects.

   

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Need Extra Help Understanding Acceleration? - The Glenbrook Physics web site does an excellent job explaining the concepts and provides good tutorial/review questions.  You can skip lesson 5, but pay special attention to lesson 6, "Kinematics equations and graphs" this lesson gives several examples of kinematics problems solved using graphs.

Review- this page gives several practice test questions along with the answers to

Graphing Practice:-this page gives more good practice questions-this time they are all

Remember if you are having trouble using your calculator to find the intersection of graphs you can go to the calculator tutorial at http://www.howardcc.edu/math/calculator/ti83frame.htm

If you are having trouble using the solver go to http://www.staff.fcps.net/kgill/The%20Equation%20Solver.doc

Additional Study Hints: The test will be over everything we have done in this unit.  The following hints and worksheets are meant to help you remember and review what we have done, they are not meant to be an exact representation of the test.

• Work the Review Sheet-- This will help you see if you understand the basics (you can skip question #2-- you won't have to draw a motion map on the test)

• Read Textbook:  Newtonian Physics, Chapter 3: Acceleration and Free Fall

• Read the Kinematics Sections 3 and 4 of the physics hyper textbook   http://hypertextbook.com/physics/mechanics/

• Look over all the old worksheets and quizzes

• Make up a x vs. t graph and see if you can draw the v vs. t and a vs. t graphs.

• Get together with your lab partners and review.

• Take the diagnostic test "Velocity and Acceleration" located at:

  http://www.spme.monash.edu.au/community/tests.html

• For more practice with kinematics graphs .....(online graphs and tracks)

  http://www.seedofknowledge.com/products/rollball/applet/applet.html

  Kinematics Equation	Comment
  	The definition of displacement in algebraic symbols- Note that "" always means "change in", and anything always means "final value - original value". Therefore, defines "change in velocity" and defines "change in time".
  	This is the definition of average velocity in mathematical symbols. (A bar over a quantity denotes "average".) Velocity is the rate position changes. Average velocity is displacement divided by time. This equation is often seen in the form , which says, essentially, "distance equals average velocity times time"
  	This is the definition of acceleration in mathematical symbols. Actually, we said that average acceleration is change in velocity divided by time, but since acceleration is constant, average acceleration and instantaneous acceleration are the same. Here are some examples of its use in solving kinematics problems.
  	This equation says that if the acceleration is constant, the average velocity in any time interval is simply the average of the original and final velocities. It is very simple to use and handy in simplifying many calculations. Its derivation requires calculus, though.
  	This equation is the good old "distance equals average velocity times time" you learned back in 5th grade - dressed up a bit! It can be very useful, particularly in conjunction with the previous equation.
  	This equation is very closely related to , and often either one can be used to solve a problem. Click here to see how this equation is used, and where it comes from.
  	This equation is useful in many situations. Here are some examples, ahd here is its derivation.
  	In many kinematics situations, you know speedometer readings, acceleration, and distance, but you don't know the time interval involved. This equation comes to the rescue in this situation. Here are some examples.

   

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