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Position versus Time
3125
2761
Mdcl1
Mdcl!
3125
2761
Mdcl1
Mdcl!
Outline
• Welcome to the x-axis
• Speeding up, Slowing down
• Graphing position versus time
• Uniform Motion
Kinematics in 1 dimension
• Kinematics is all about predicting where an object will be in the future
• Kinematics doesn’t tell us about WHY an object is moving, only WHERE
• 1-D motion describes motion that is constrained to move along a line
• To describe motion in 1 dimension, a coordinate system must be created
As opposed to WHY an object moves
As opposed to WHY an object moves
What do you need for a 1-D coordinate system
What do you need for a 1-D coordinate system
x [
m]
t [s]
Walk–No Motion
Describe the path
x [
m]
t [s]
Walk–Const +ve Speed
Describe the path
x [
m]
t [s]
Walk–Const –ve Speed
Describe the path
x [
m]
t [s]
Walk–Back/Forth
Describe the path
x [
m]
t [s]
Walk–Back/Forth
Walk the path
x [
m]
t [s]
Walk–Two +ve Speeds
Describe the path
The slope of a position vs. time graph tells us an object’s speed. Why?
12
12
xtvx
tvxxt
xv
avg
avg
avg
This equation has a familiar form… bmxy
QQ12: x vs. t
Quick Quiz: John leaves class and walks in a straight line directly toward his residence. He starts at a position which is 300 m away from the residence, and walks at a constant speed. After 150 s, he arrives at his residence. Which of the following position-time graphs represents his motion over this period, if his residence is at the origin?
x [m]
t [s]
300
01500
x [m]
t [s]
300
01500 x [m]
t [s]
300
01500
x [m]
t [s]
300
01500
A.
B.
C.
D.
QQ13: simultaneity Quick Quiz: At the moment that John leaves class,
Monica leaves the residence and heads directly toward the classroom that John is leaving. Having walked there before, Monica knows that the trip would take her exactly 100 s.
At what time does Monica bump into John?
A. 60s
B. 100s
C. 150s
D. Not enough information to know for sure.
Answer QQ13
The d-t graph
x [m]
t [s]
300
01500 100
John
Mon
ica
Solution:
QQ14: speed
A parachutist opens her parachute at an altitude of 1500 m. She then descends slowly to earth at a steady speed of 5 m/s. Sketch a position versus time graph for her motion. Start your graph as her parachute opens.
(There are enough numbers here that you can make a real graph. Include values for the x and t intercepts)
Example
QQ15: intersection
Quick Quiz: At what time do objects A & B have the same speed?
x [
m]
t [s]1 2 3 4
A
B
A. 0s B. 3s C. never D. all the time
Do for next class:
• Read: sections 2.3, 2.4 (don’t worry about the integrals, but be sure to understand Stop To Think 2.3)
• Suggested problems: 2.10, 2.11