KinematicsKinematics - The branch of classical mechanics that describes the motions of points, bodies (objects) and systems of bodies (groups of objects) without consideration of the causes of motion. Mechanics Lecture 1, Slide 1 Kinematics

Classical Mechanics Lecture 1 Today's Concepts: a) Displacement, Velocity, Acceleration b) 1-D Kinematics with constant acceleration Mechanics Lecture 1, Slide 2 If you haven't done Prelecture 1 yet, please do so later today

Pre-lecture Viewing Times Mechanics Lecture 1, Slide 3 Slide 1: 1.10 min Slide 2: 2.27 min Slide 3: 1.98 min Slide 4: 1.83 min Slide 5: 2.03 min Slide 6: question Slide 7: 2.17 min Slide 8: 2.12 min Slide 9: question Slide 10: 1.85 min Slide 11: 0.87 min Minimum Total Viewing time = 16.2 minutes Good!???!

Mechanics Lecture 1, Slide 4 Lecture Thoughts

Main Points of Unit 1 Mechanics Lecture 1, Slide 5

Main Points of Unit 1 Mechanics Lecture 1, Slide 6

Mechanics Lecture 1, Slide 7 Prelecture Example Displacement

Mechanics Lecture 1, Slide 8 Prelecture Example Displacement

Mechanics Lecture 1, Slide 9 Displacement Time taken Displacement and Velocity in One Dimension But what about ?

Mechanics Lecture 1, Slide 10 Definition: Speed = |v(t)| The v(t) vs. t plot is just the slope of the x(t) vs. t plot Displacement and Velocity in One Dimension The slope of the x(t) vs. t plot is the “derivative” of x(t) w.r.t t. Limit of  t  0

Mechanics Lecture 1, Slide 11 Displacement and Velocity in One Dimension

The Derivative Mechanics Lecture 1, Slide 12

The Derivative Mechanics Lecture 1, Slide 13 BUILD FROM HERE…

Mechanics Lecture 1, Slide 14 Displacement as a function of velocity

The Definite Integral Mechanics Lecture 1, Slide 15

The Definite Integral Mechanics Lecture 1, Slide 16

The Definite Integral Mechanics Lecture 1, Slide 17 Integral : “Anti-derivative”

Displacement and Velocity in one dimension A. Yes B. NO Mechanics Lecture 1, Slide 18 Are the plots shown at the left correctly related?

Prelecture Question 1 Mechanics Lecture 1, Slide 19

Prelecture Question 1 Mechanics Lecture 1, Slide 20

Prelecture Help Question 1 Mechanics Lecture 1, Slide 21

Mechanics Lecture 1, Slide 22 For the Displacement and Velocity curves shown on the left, which is the correct plot of acceleration vs. time? A B Checkpoint 1

Mechanics Lecture 1, Slide 23 A B Correct answer Checkpoint 1

Mechanics Lecture 1, Slide 24 Checkpoint 1-responses

Mechanics Lecture 1, Slide 25 Checkpoint 1-responses

Mechanics Lecture 1, Slide 26 The velocity vs. time plot of some object is shown to the right. Which diagram below could be the Displacement vs. time plot for the same object? ABC Clicker Question

Which Plot? A. Plot A B. Plot B C. Plot C D. None of the above Mechanics Lecture 1, Slide 27 ABC

Mechanics Lecture 1, Slide 28 The velocity vs. time plot of some object is shown to the right. Which diagram below could be the Displacement vs. time plot for the same object? ABC Clicker Question

Mechanics Lecture 1, Slide 29 Acceleration

Velocity,Acceleration Signed quantity Mechanics Lecture 1, Slide 30

Velocity,Acceleration Signed quantity Mechanics Lecture 1, Slide 31 negative acceleration Car slowing down while moving in + direction a<0 Car slowing down while moving in - direction a>0

Prelecture Question 2 Mechanics Lecture 1, Slide 32

Prelecture Question 2 Mechanics Lecture 1, Slide 33

Motion with Constant Acceleration Mechanics Lecture 1, Slide 34

Motion with Constant Acceleration Velocity vs displacement Mechanics Lecture 1, Slide 35 Let’s eliminate time…to obtain v(x) for special case of constant acceleration

Mechanics Lecture 1, Slide 36 Motion with Constant Acceleration constant a(t) = a

Mechanics Lecture 1, Slide 37 At t = 0 a ball, initially at rest, starts to roll down a ramp with constant acceleration. Suppose it moves 1 foot between t = 0 sec and t = 1 sec. How far does it move between t = 1 sec and t = 2 sec ? A) 1 foot B) 2 feet C) 3 feet D) 4 feet E) 6 feet Checkpoint 2

Mechanics Lecture 1, Slide 38 1ft 4ft 9ft ? 16ft At t = 0 a ball, initially at rest, starts to roll down a ramp with constant acceleration. Suppose it moves 1 foot between t = 0 sec and t = 1 sec. How far does it move between t = 1 sec and t = 2 sec ? A) 1 foot B) 2 feet C) 3 feet D) 4 feet E) 6 feet Checkpoint 2

Mechanics Lecture 1, Slide 39 Checkpoint 2 Responses

Mechanics Lecture 1, Slide 40 Checkpoint 2 Responses

Mechanics Lecture 1, Slide 41 1ft 4ft 9 ft 3 16f t Checkpoint 2 Solution

Summary Mechanics Lecture 1, Slide 42

Summary Mechanics Lecture 1, Slide 43 Direct Relationship between velocity and displacement (time dependence removed) for special case of constant acceleration

Acceleration Mechanics Lecture 1, Slide 44 mID=192801&enrollmentID=29042

Schaum’s Outline Mechanics Lecture 1, Slide 45

Displacement,Velocity & Acceleration Mechanics Lecture 1, Slide 46 Need to become comfortable with displacement, velocity and acceleration and how they are related!!!

Constant Acceleration Mechanics Lecture 1, Slide 47

Mechanics Lecture 1, Slide 48

Hyperphysics-Motion Mechanics Lecture 1, Slide 49

Hyperphysics-Motion Mechanics Lecture 1, Slide 50

Hyperphysics Motion Mechanics Lecture 1, Slide 51 Displacement vs timet Velocity vs timet Acceleration vs timet

Hyperphysics Motion Mechanics Lecture 1, Slide 52

Main Points of Unit 1 Mechanics Lecture 1, Slide 53

Main Points of Unit 1 Mechanics Lecture 1, Slide 54

A “real world” ramp experiment Mechanics Lecture 1, Slide 55 Kilometre lance

A “real world” ramp experiment Mechanics Lecture 1, Slide 56 Could not find elapsed times…to check. Assume constant acceleration Verbier- Mont Fort