Mr. Rogers AP Physics C Study Guide  --   Kinematics

Unit Plan Practice Test Study Guide

Podcast (MP3 file): Physics With Mr. R - The Foundations of Classical Physics

Click on the above link to hear Mr. Rogers discuss the foundations of classical physics, including many of the subjects relevant to this chapter (approximate play time = 17 minutes). For a transcript of the above, click here (pdf file).

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Mathematical models

Basic Mathematical Definitions Equations for Constant Acceleration (Note: The 2 equations listed below only work for constant acceleration)
   speed = (distance) / (time)   x = 1/2at2 + vot + xo
  a = dv/dt   v = at + vo
  v = dx/dt
Calculus - derivative of a polynomial Calculus - integration of a polynomial
Finds the slope at a point
  Finds the area under a curve
  d   (uxn)  =  nux(n-1)
  ∫u xn dx = u/(n+1) x (n+1) + C  for n!=1

Key Principles

Assume planet Earth and no air resistance for the following:

  1. Derivative: the slope at a point.
  2. Integral: the area under the curve between two values.
  3. The negative sign on a vector indicates direction. It does not indicate that an object is slowing down.
  4. How to determine if an object is slowing down or speeding up: 
  • Speeding up: the acceleration vectors go in the same direction
  • Slowing down: the acceleration vectors go in opposite directions.
  1. Acceleration due to Gravity: On the surface of a planet, objects all fall at the same acceleration if air resistance is negligible, regardless of their mass.
  • Drop an object, throw it up, throw it down and it still accelerates at the same rate, 9.8 m/s/s downward.
  • Throw an object upward and it will reach zero velocity at the top of its path but the acceleration is still 9.8 m/s/s downward.
  1. Models: Physics is about model building. Models always have errors due to simplifying assumptions.
  2. Freefalling objects: ignoring air resistance, free falling objects accelerate downward with a rate = g. By definition, they only have a force of gravity acting on them.
  3. Effects of air resistance on a dropped object: The velocity starts at zero and reaches a constant value called terminal velocity. The acceleration starts at one g and goes to zero at terminal velocity

Key Principles

Coin Flip Problem: Albert flips a coin up in the air at an upward velocity of 5 m/s. He fails to catch it on the way down and it falls down an 8 m deep well. Draw a vs t, v vs t, and y vs t curves. Calculate the max height and max magnitude of velocity of the coin. Batmobile Problem: Batman fires up the the Batmobile and roars off with an acceleration = 5t + 10. Draw the a vs t and v vs t plot. Find the final velocity of Batman and how far he travels in 2 seconds.
Falling With Air Resistance: Compare the the a vs.t, v vs. t, x vs. t curves with air resistance to those without for a dropped object. Two-Part Kinematics Problem: Starting from rest Martha accelerates her motor cycle forward at 5 m/s2 for ten seconds then accelerates backwards at 2 m/s2 for ten seconds. How fast is she going at the end of the 20 second time span described above? How far has she traveled?  Sketch the a vs.t, v vs. t, x vs. t graphs.
Graphical Integration: Given a graph of acceleration vs. time solve for velocities and displacements. Graphical Derivatives: Given a graph of displacement vs. time solve for velocities and accelerations.



acceleration (vector) frame of reference speed (scalar)
derivative integration scalar
displacement (vector) kinematics velocity (vector)
distance (scalar)

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