Lecture 01: 1D Kinematics - AstronomyBelz/Phys2210/Lecture01.pdfLecture 01: 1D Kinematics Physics 2210 ... Velocity, Acceleration b) 1-D Kinematics with constant acceleration. Mechanics

Lecture 01: 1D Kinematics

Physics 2210Fall Semester 2014

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Alles Leben ist Problemlösen

- Karl Popper

“Supplemental Readings” link on course webpage:

I will post Main Points for each SP

Chapter

“Supplemental Readings” link on course webpage:

Equation Sheet

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Monday 09:00 – 11:00 AM Amaya

Tuesday 12:00 – 01:00 PM Nick

Wednesday 09:30 – 11:30 AM Jason

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Unit 1 Feedback

● Thanks for your comments!

● Main points:● Definition of

acceleration, esp. negative acceleration.

● Interpreting graphs● Checkpoint #2● Calculus practice● Examples

Kinematics: n. The branch of mechanics that studies the motion of a body or a system of

bodies without consideration given to its mass or the forces acting on it.

www.thefreedictionary.com

Mechanics Lecture 1, Slide 7

Today's Concepts:a) Displacement, Velocity, Accelerationb) 1-D Kinematics with constant acceleration

Mechanics Lecture 1, Slide 8

Displacement and Velocity in One Dimension

Displacement, time interval finite

Displacement, time interval infinitesimal

Flashcard Questions

Mechanics Lecture 1, Slide 10

A) YESB) NO

Are the plots shown at the left correctly related?

Displacement and Velocity in One Dimension

Mechanics Lecture 1, Slide 11

A) YESB) NO

Are the plots shown at the left correctly related?

Displacement and Velocity in One Dimension

Mechanics Lecture 1, Slide 12

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?

A B C

Mechanics Lecture 1, Slide 13

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?

A B C

Mechanics Lecture 1, Slide 14

Acceleration

For the Displacement and Velocity curves shown on the left, which is the correct plot of acceleration vs. time?

AA

BB

Checkpoint 1:

Mechanics Lecture 1, Slide 16

AA

BB

The object slowed down (negative acceleration) and at the midpoint sped up (positive acceleration).

Acceleration is negative while the velocity decreases and it is positive as the velocity increases

Typical B answers

Checkpoint #1 Results

Mechanics Lecture 1, Slide 17

Constant Acceleration

constanta(t) = a

Example

a) Plot a graph of the acceleration vs time

b) Determine the average acceleration for 5 s < t < 15 s and

c) for 0 < t < 20 s.

A velocity-time graph for an object moving along the x axis is shown in the figure.

Mechanics Lecture 1, Slide 18

Suggested Problem Solving Template

1) Keep calm, and...

2) Read the problem carefully.

3) Draw a diagram w/ coordinates.

4) List knowns.

5) List unknowns.

6) Find equation linking knowns & unknowns.

7) Solve the equation.

8) Repeat as needed.

Mechanics Lecture 1, Slide 20

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 21

1ft4ft

9ft

3'

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 22

1ft4ft

9ft

3'

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 23

Acceleration is one foot per second, using displacement equation with accel as a constant gives us x = 0+0+.5*1*2^2 = 2

The ball has an acceleration of 1ft/s^2. So, for every second that the ball is moving, it gains another 1ft/s of velocity.

Typical B answers

1ft4ft

9ft

3

16ft

Checkpoint 2 Responses

Checkpoint 2 Follow-up

The ball is now rolled up the same ramp. It is given an initial speed of 10 feet/second. How far will it roll before stopping, and then rolling back down the ramp? Ans: 25 feet

Example

A hare and a tortoise race over a straight course, 1.00 km long. The tortoise crawls at a speed of 0.200 m/s toward the finish line. The hare runs at a speed of 8.00 m/s toward the finish line for 0.800 km and then stops while the tortoise passes. The hare then resumes running at 8.00 m/s, and the hare and the tortoise cross the finish line at the same time.

a) How far is the tortoise from the finish line when the hare resumes running?

b) For what time interval was the hare stationary?

a) 25 metersb) 4,875 seconds

Example

A ball is thrown upwards with an initial speed of 3.0 meters/second. How far will it rise before it comes to rest, and then falls back down?

(Assume the acceleration due to gravity g = 9.81 m/s2, and negligible air resistance.)

0.459 meters