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. 5.1Graphing 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– Data from a Position-Time Graph

• Pg. 84– 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……..

• 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. 88Example 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. 13-15

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. 5-13 Pg. 96

• Practice Problems….

• Pg. 97

• Pr. 17-22

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