Week 3 - Chapter 2 - Kinematics Part 2 Flashcards
What are the simplified expression for time, displacement, and velocity? Don’t forget to annotate what the subscripts mean.
What assumption will we make with acceleration that identify average and instantaneous accelerations as equal?
Assume that acceleration is constant.
For one thing, acceleration is constant in a great number of situations.
Furthermore, in many other situations we can accurately describe motion by assuming a constant acceleration equal to the average acceleration for that motion.
Finally, in motions where acceleration changes drastically, such as a car accelerating to top speed and then braking to a stop, the motion can be considered in separate parts, each of which has its own constant acceleration.
How do you solve for average velocity when acceleration is constant?
How do you solve for the final position, x, when using the initial position, x0, average velocity, and time?
What does the equation x = x0 +vt illuminate about the relationship between displacement, velocity and time?
Displacement is a linear function of average velocity!
What is the equation for final velocity by manipulating the definition of acceleration?
Insight on the relationship among velocity, acceleration, and time
- Final velocity depends on how large the acceleration is and how long it lasts
- If acceleration is zero, then the final velocity equals the initial velocity (v = v0), as expected (i.e., velocity is constant)
- If a is negative, then the final velocity is less than the initial velocity
How do you solve for final position when velocity is not constant (a does not equal 0)?
By examine this equation we see:
- Displacement depends on the square of elapsed time when acceleration is not zero. For the dragster example, the dragsters covers only one fourth of the total distance in the first half of the elapsed time.
- If acceleration is zero, then the initial velocity equals average velocity
How do you solve for final velocity when velocity is not constant?
You will probably use the square root to reduce powers of meter or seconds or etc. Notice how the final velocity is squared hence the square root.
By examining this equation:
- The final velocity depends on how large the acceleration is the distance over which it acts
- For a fixed deceleration, a car that is going twice as fast doesn’t simple stop in twice the distance–it takes much further to stop. (this is why we have reduced speed zones near schools)
Summary of Kinematic Equations (constant a) Review
None
When solving for time using the equation for final position when velocity is not constant, what may you have to do?
What is the equation?
You the quadratic formula to solve the equation! There are multiple ways to do this.
Problem-Solving Steps (Flip for more steps)
- Examine the situation to determine which physical principles are involved.
It often helps to draw a simple sketch at the outset. You will also need to decide which direction is positive and note that on your sketch. Once you have identified the physical principles, it is much easier to find and apply the equations representing those principles. Although finding the correct equation is essential, keep in mind that equations represent physical principles, laws of nature, and relationships among physical quantities. Without a conceptual understanding of a problem, a numerical solution is meaningless.
- Make a list of what is given or can be inferred from the problem as stated (identify the knowns).
Many problems are stated very succinctly and require some inspection to determine what is known. A sketch can also be very useful at this point. Formally identifying the knowns is of particular importance in applying physics to real-world situations. Remember, “stopped” means
velocity is zero, and we often can take initial time and position as zero.
- Identify exactly what needs to be determined in the problem (identify the unknowns).
In complex problems, especially, it is not always obvious what needs to be found or in what sequence. Making a list can help.
- Find an equation or set of equations that can help you solve the problem.
Your list of knowns and unknowns can help here. It is easiest if you can find equations that contain only one unknown—that is, all of the other variables are known, so you can easily
solve for the unknown. If the equation contains more than one unknown, then an additional equation is needed to solve the problem. In some problems, several unknowns must be determined to get at the one needed most. In such problems it is especially important to keep physical principles in mind to avoid going astray in a sea of equations. You may have to use two (or more) different equations to get the final answer.
- Substitute the knowns along with their units into the appropriate equation, and obtain numerical solutions complete with units.
This step produces the numerical answer; it also provides a check on units that can help you find errors. If the units of the answer are incorrect, then an error has been made. However, be warned that correct units do not guarantee that the numerical part of the answer is also correct.
- Check the answer to see if it is reasonable: Does it make sense?
This final step is extremely important—the goal of physics is to accurately describe nature. To see if the answer is reasonable, check both its magnitude and its sign, in addition to its units.
Your judgment will improve as you solve more and more physics problems, and it will become possible for you to make finer and finer judgments regarding whether nature is adequately described by the answer to a problem. This step brings the problem back to its conceptual meaning. If you can judge whether the answer is reasonable, you have a deeper understanding of physics than just being able to mechanically solve a problem.
When solving problems, we often perform these steps in different order, and we also tend to do several steps simultaneously. There is no rigid procedure that will work every time. Creativity and insight grow with experience, and the basics of problem solving become almost automatic. One way to get practice is to work out the text’s examples for yourself as you read. Another is
to work as many end-of-section problems as possible, starting with the easiest to build confidence and progressing to the more difficult. Once 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.
What is defined as an object falling without air resistance or friction?
Free-fall.
The force of gravity causes objects to fall toward the center of earth and this acceleration of free-falling objects is called?
Acceleration due to gravity and this constant, which means we can apply the kinematics equations to any falling object where air resistance and friction are negligible.
What is the symbol for gravity and its average value at any given location on earth?
g = 9.80 m/s^2
One-dimensional Motion Involving Gravity
- Considering straight up and down motion with no air resistance or friction (much like our work not incorporating g = a)
- Velocity in these cases with be vertical, which is what gravity defines, and if the object is dropped, we know the initial velocity is zero. Once the object leaves contact it is in free fall.
- The motion is one-dimensional and has constant acceleration of magnitude g.
- Representing vertical displacement with the symbol y and use x for horizontal displacement.
When two physical quantities are plotted against each other, which axis is an independent variable and which is a dependent variable?
What is a straight line graph in the general form of? What do the letters mean?
The horizontal axis is considered independent, and the vertical axis is considered dependent.
y = mx + b. m is the slope and is defined to be the rise divided by the run of the straight line. The letter b is used for y-intercept, which is the point at which the line crosses the vertical axis.
How do you find the slope (velocity) of a curve at a point of a position over time graph?
It is equal to the slope of a straight line tangent to the curve at that point!
Determine the endpoints of the tangent line (x, y) and (x, y). Calculate the slope aka velocity by using the formula.
