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