2.6 Problem-Solving Basics for One-Dimensional Kinematics

2.6 Problem-Solving Basics for One-Dimensional Kinematics

  • A rocket is in the air.
  • Choose an equation that will allow you to solve for time.
  • Rearrange to find a solution.
  • You need problem-solving skills to succeed in physics.
    • The ability to apply broad physical principles, usually represented by equations, to specific situations is a very powerful form of knowledge.
    • It's more powerful than a list of facts.
    • Analytical skills and problem-solving abilities can be applied to new situations, whereas a list of facts cannot be made long enough to contain every possible circumstance.
    • Analytical skills can be used to solve problems in this text and to apply physics in everyday life.
  • The following general procedures facilitate problem solving and make it more meaningful, because there is no simple step-by-step method that works for every problem.
    • A lot of creativity and insight is required.
  • Determine which physical principles are involved in the situation.
    • It is helpful to draw a simple sketch at the beginning.
  • On your sketch, you will need to decide which direction is positive.
    • It is much easier to find and apply the equations for the principles once you have identified them.
    • Although finding the correct equation is important, keep in mind that equations represent physical principles, laws of nature, and relationships among physical quantities.
    • A numerical solution is meaningless if there is no conceptual understanding of the problem.
  • A list of what can be inferred from the problem can be made.
    • Many problems need to be inspected to determine what is known.
    • At this point, a sketch can be very useful.
    • Applying physics to real-world situations requires formal identification of the knowns.
    • "Stopped" means zero, and we can often take initial time and position as zero.
  • Identifying the unknowns will help determine exactly what needs to be determined in the problem.
    • It is not always obvious what needs to be found in a problem.
    • A list can help.
  • You can find an equation or set of equations to solve the problem.
    • Your list of knowns and unknowns can help here.
    • If you can find equations with only one unknown, you can easily solve them for the unknown.
    • An additional equation is needed to solve the problem if the equation contains more than one unknown.
    • Several unknowns must be determined to get to the one needed most in some problems.
    • It is important to keep physical principles in mind to avoid going astray in a sea of equations.
    • You may have to use more than one equation to get the answer.
  • Get numerical solutions complete with units by substituting the knowns along with their units into the equation.
    • The check on units that can help you find errors is provided by this step.
    • An error has been made if the units of the answer are incorrect.
    • Correct units don't guarantee that the numerical part of the answer is correct.
  • The goal of physics is to accurately describe nature.
    • To find out if the answer is reasonable, check both its magnitude and sign.
  • As you solve more and more physics problems, your judgement will improve and you will be able to make better judgements about nature.
    • The problem is brought back to its conceptual meaning by this step.
    • You have a deeper understanding of physics if you can judge whether the answer is reasonable.
  • We tend to do several steps at the same time when we solve problems.
  • There isn't a procedure that will work every time.
    • The basics of problem solving become almost automatic with experience.
    • As you read the text, you can work out the examples for yourself.
    • One way to work as many end-of-section problems as possible is to start with the easiest to build confidence.
    • When you become involved in physics, you will see it all around you, and you can begin to apply it to situations you encounter outside the classroom, just as is done in many of the applications in this text.
  • Nature must be described accurately.
    • Some problems have results that are unreasonable because of one premise or another.
    • An unreasonable result is produced by the physical principle being applied correctly.
    • If a person starts a foot race at 100 s, his final speed will be 40 m/s (about 150 km/h), which is clearly unreasonable because the time of 100 s is an unreasonable premise.
    • There is more to describing nature than just manipulating equations.
    • Checking the result of a problem to see if it is reasonable helps uncover errors in problem solving and builds intuition in judging nature.
  • The following strategies can be used to determine whether an answer is reasonable or not.
  • The strategies outlined in the text can be used to solve the problem.
    • You can use the equation below to find the unknown final velocity if you identify the givens as the acceleration and time.
  • Check to see if the answer is reasonable.
    • You may need to convert meters per second into miles per hour.
  • It's too large because it's four times greater than a person can run at.