# Ch. 5 A Mathematical Model of Motion

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Ch. 5 A Mathematical Model of Motion
Milbank High School

Objectives Study average and instantaneous velocity along with acceleration. Use graphs and equations to solve problems involving moving objects, including free falling objects.

Ch. 5.1 Graphing Motion in One Dimension
Objectives Interpret graphs of position versus time for a moving object to determine the velocity of the object Describe in words the information presented in graphs and draw graphs from descriptions of motion Write equations that describe the position of an object moving at constant velocity

Position vs. Time Graphs
It’s obvious! Plots the position vs the time of an object. Velocity in this graph is constant!

Is it always constant? No!

Constant vs. Changing

Two or more objects

Ex. Problems Pg. 83 Pg. 84 Pg. 85 Data from a Position-Time Graph
Interpreting Position-Time Graphs Pg. 85 Describing Motion from a Position-Time Graph

Uniform Motion Means that equal displacements occur during successive equal time intervals Pg 86, Fig 5-6

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.

What is the slope? Rise = -24 m Run = 8 seconds Slope = -3 m/s

What is the slope? Rise = 20s Run = 5m Slope = 4 m/s

Using Equations While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed?

Or…….. t = any value of time d = position at that time
We can eliminate t0 Position with constant velocity d = d0 + vt t = any value of time d = position at that time d0 = position at t = 0 v = velocity Pg. 88 Example Problem

Practice! Pg. 85 Pr. 1-3 Pg. 87 Pr. 4-8 Pg. 89 Pr. 9-12

Sec 5.2 Graphing Velocity in One Dimension
Basically like 5.1, except velocity isn’t always constant. Objectives Determine, from a graph of velocity versus time, the velocity of an object at a specified time Interpret a v-t graph to find the time at which an object has a specific velocity Calculate the displacement of an object from the area under a v-t curve.

Determining Instantaneous Velocity
Draw a line tangent to the curve The smaller the time interval, the more precise your slope is The smaller the time ratio, the closer to the instantaneous velocity you will come

Velocity-Time Graphs It’s obvious! Plots the velocity vs. the time
Gives no information about the position

Is the velocity constant?

Displacement from a Velocity-Time Graph
v = ∆d/∆t so….. ∆d = v∆t

Practice… Pg. 93 Pr

Sec. 5.3 Acceleration Determine from the curves on a velocity-time graph both the constant and instantaneous acceleration Determine the sign of acceleration using a v-t graph and a motion diagram Calculate the velocity and the displacement of an object undergoing constant acceleration

Which cars are accelerating??

Acceleration The rate of change of velocity divided by time change
Usually m/s/s…..or m/s2

Constant and Instantaneous Acc.
Constant-straight line on a v-t graph Instantaneous-find the slope at a certain point on a v-t graph Ex. Pg. 95

Positive and Negative Acceleration

Positive and Negative Acceleration
The sign of the acceleration depends upon the chosen coordinate system Fig Pg. 96 Practice Problems…. Pg. 97 Pr

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 system Use the motion equations to solve problems involving freely falling objects

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

Acceleration due to gravity
The acceleration of an object in free fall that results from the influence of the Earth’s gravity