Presentation on theme: "Ch. 5 A Mathematical Model of Motion"— Presentation transcript:
1 Ch. 5 A Mathematical Model of Motion Milbank High School
2 ObjectivesStudy average and instantaneous velocity along with acceleration.Use graphs and equations to solve problems involving moving objects, including free falling objects.
3 Ch. 5.1 Graphing Motion in One Dimension ObjectivesInterpret graphs of position versus time for a moving object to determine the velocity of the objectDescribe in words the information presented in graphs and draw graphs from descriptions of motionWrite equations that describe the position of an object moving at constant velocity
4 Position vs. Time Graphs It’s obvious!Plots the position vs the time of an object.Velocity inthis graph isconstant!
9 Ex. Problems Pg. 83 Pg. 84 Pg. 85 Data from a Position-Time Graph Interpreting Position-Time GraphsPg. 85Describing Motion from a Position-Time Graph
10 Uniform MotionMeans that equal displacements occur during successive equal time intervalsPg 86, Fig 5-6
11 Determining the Slope of a Line Pick two points on the line and determine their coordinates.Determine the difference in y-coordinates of these two points (rise).Determine the difference in x-coordinates of these two points (run).Divide the difference in y-coordinates (rise) by the difference in x-coordinates (run).Slope = rise/run.
13 What is the slope?Rise = -24 mRun = 8 secondsSlope = -3 m/s
14 What is the slope?Rise = 20sRun = 5mSlope = 4 m/s
15 Using EquationsWhile on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed?
16 Or…….. t = any value of time d = position at that time We can eliminate t0Position with constant velocityd = d0 + vtt = any value of timed = position at that timed0 = position at t = 0v = velocityPg. 88Example Problem
18 Sec 5.2 Graphing Velocity in One Dimension Basically like 5.1, except velocity isn’t always constant.ObjectivesDetermine, from a graph of velocity versus time, the velocity of an object at a specified timeInterpret a v-t graph to find the time at which an object has a specific velocityCalculate the displacement of an object from the area under a v-t curve.
19 Determining Instantaneous Velocity Draw a line tangent to the curveThe smaller the time interval, the more precise your slope isThe smaller the time ratio, the closer to the instantaneous velocity you will come
20 Velocity-Time Graphs It’s obvious! Plots the velocity vs. the time Gives no information about the position
24 Sec. 5.3AccelerationDetermine from the curves on a velocity-time graph both the constant and instantaneous accelerationDetermine the sign of acceleration using a v-t graph and a motion diagramCalculate the velocity and the displacement of an object undergoing constant acceleration
29 Positive and Negative Acceleration The sign of the acceleration depends upon the chosen coordinate systemFig Pg. 96Practice Problems….Pg. 97Pr
30 5.4 Free Fall Recognize the meaning of acceleration due to gravity Define the magnitude of the acceleration due to gravity as a positive quantity and determine the sign of the acceleration relative to the chosen coordinate systemUse the motion equations to solve problems involving freely falling objects
31 Gravity Symbol - - “g” Acceleration due to gravity= 9.80m/s2 Be aware of the signs……if upward is your positive direction, then g is going to be negative
32 Acceleration due to gravity The acceleration of an object in free fall that results from the influence of the Earth’s gravity