Describing Motion: Kinematics in One Dimension PowerPoint Presentation, PPT - DocSlides

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Slide1

Describing Motion: Kinematics in One Dimension

AP Physics

Chapter 2

Slide2

Describing Motion: Kinematics in One Dimension

AP Physics

Section 2-1 Reference Frames and Displacement

Slide3

Describing Motion: Kinematics in One Dimension

IA1a -

Students should understand the general relationships among position, velocity, and acceleration for the motion of a particle along a straight line

2-1

Slide4

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Mechanics – study of

motion, force, energy

Kinematics – how objects move

Dynamics – why objects move

Translational Motion – move without rotation

2-1

Slide5

Reference Frames (Frames of Reference)Are we moving?Compared to what?Usually with “respect to the Earth”

Unless otherwise specifiedAll other cases, must specify the frame of referenceTypically done with coordinate grid and x and y axis (only x or y for 1D motion)

2-1

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide6

Positive – up and rightNegative – down and left

2-1

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide7

Defining Motion

Position – relative to frame of reference (x or y)

Displacement – change in position (meters) D

x = x

2

-x

1

Not distance

2-1

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide8

Distance vs. Displacement

2-1

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide9

Distance – scalar (magnitude)Displacement – vector (magnitude and direction)Must give a directionEast/West, up/down

2-1

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide10

AP PhysicsSection 2-2 Average Velocity

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide11

2-1

Distance Time Graph Gizmo

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide12

Average Speed – distance per unit time (scalar)

Average Velocity – displacement per unit time (vector)(meters/second)

Dx = displacement

D

t = change in time

2-2

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide13

2-2

Distance Time Velocity Graph Gizmo

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide14

AP PhysicsSection 2-3 Instantaneous Velocity

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide15

Instantaneous Velocity – the average velocity during an infinitesimally short time intervalWe will only calculate situations with constant velocity or constant acceleration

Calculus is required if acceleration is not constant

2-3

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide16

Slope of any displacement time graph is the instantaneous velocity

2-3

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide17

Using the graph calculate the average velocity between t0

=2 and t=5APP-Matt-09

S-2

Slide18

Average Acceleration – change in velocity per unit time (vector) (meters/second2)

v is final velocityv0

is initial velocity (or at time 0)Sign of a indicates direction of vectorDeceleration is just negative acceleration

2-4

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide19

AP PhysicsSection 2-4 Acceleration

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide20

Acceleration is the slope of the velocity time graph

2-4

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide21

AP PhysicsSection 2-5 Motion at Constant Acceleration

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide22

Describing Motion: Kinematics in One Dimension

IA1b -

Students should understand the special case of motion with constant acceleration.

2-4

Slide23

Describing Motion: Kinematics in One Dimension

We are limited to calculations when acceleration is a constant

We will use the mathematical definition of displacement, velocity, and acceleration to derive 4 Kinematic equations.

Memorize these equations – you will use them a lot

2-5

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide24

Describing Motion: Kinematics in One Dimension

Assume

t

0

= 0, it drops out of equations

We rework the definition of acceleration to get our first working equation

2-5

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide25

Describing Motion: Kinematics in One Dimension

For the second equation we first rework the definition of average velocity to solve for displacement

2-5

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide26

Describing Motion: Kinematics in One Dimension

We define average velocity as the average of the initial and final velocity (only possible with constant acceleration)

2-5

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide27

Now we combine the last three equations

2-5

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide28

For the third equation we start by using a version of the definition of velocity

2-5

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide29

Combine with our average velocity definition

2-5

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide30

Describing Motion: Kinematics in One Dimension

Solve the definition of acceleration for time

2-5

Slide31

Describing Motion: Kinematics in One Dimension

Combine and you get

2-5

Slide32

Finally, solve for final velocity

2-5

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide33

The 4

th equation is not found in your book, but is in most others

2-5

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide34

AP PhysicsSection 2-6 Solving Problems

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide35

Determine what the object is you are solving for.Draw a diagram. Determine the positive and negative direction for motion.

Write down any known quantities.Think about “The Physics” of the problem.

Determine what equation, or combination of equations will work under these Physics conditions.

2-6

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide36

Make your calculations.See if your answer is reasonable.

Determine what units belong with the number, and what the direction should be if it is a vector.

2-6

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide37

A car slows down uniformly from a speed of 21.0 m/s to rest in 6.00s. How far did it travel in this time?Object – car

Diagram

2-6

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide38

A car slows down uniformly from a speed of 21.0 m/s to rest in 6.00s. How far did it travel in this time?Object – car

DiagramKnow v

0=21.0m/s v=0m/s

t=6.00s

2-6

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide39

A car slows down uniformly from a speed of 21.0 m/s to rest in 6.00s. How far did it travel in this time?Physics – car is going through negative acceleration in 1D, acceleration is constant

Equation – needs v0,

v, t, x (define x0=0) So

2-6

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide40

A car slows down uniformly from a speed of 21.0 m/s to rest in 6.00s. How far did it travel in this time?Physics – car is going through negative acceleration in 1D, acceleration is constant

Equation – needs v0,

v, t, x (define x0=0) Solve

2-6

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide41

A car is behind a truck going 25m/s on the highway. The car’s driver looks for an opportunity to pass, guessing that his car can accelerate at 1.0m/s2. He gauges that he has to cover the 20 m length of the truck, plus 10 m clear room at the rear of the truck and 10 m more at the front of it. In the oncoming lane, he sees a car approaching, probably also traveling at 25 m/s. He estimates that the car is about 400 m away. Should he attempt to pass?

2-6

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide42

Object – carDiagram

Known quantitiesCar relative truck Car relative to App. Car

v0=0m/s 25m/s a=1m/s

2

1m/s

2

x=40m

4. Physics – The car travels 40m relative to the truck to complete the pass, but it will travel further relative to the approaching car. We must find how far and see if the position of the two cars overlaps

2-6

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide43

5. Time for car to pass

2-6

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide44

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

5. How far did the car travel?

 

Slide45

5. How far did the other car get in that time?

2-6

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Can you say ‘boom?’

Slide46

A lonely rabbit is standing 30 m from a really cute bunny that is hopping away at a constant 10 m/s. If the rabbit starts from rest, and can accelerate at 5 m/s2,

How long will it take to reach the bunnyHow far will he have traveledHow much faster than the bunny will he be running

S-3

Slide47

AP PhysicsSection 2-7 Falling Objects

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide48

We will ignore air frictionWe will learn the why later.Acceleration due to gravity at Earth’s surface is 9.80 m/s

2 directed downward (-9.80m/s2)Symbol g

represents acceleration due to gravityStill use motion equations but x is replaced with y

a is replaced with

g

2-7

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide49

Two common misconceptionAcceleration and velocity are always in the same direction a. No, as an object is thrown upward, velocity is +y, acceleration is –y

Acceleration is zero at the highest point. a. No, at the highest point, the velocity is zero, but acceleration is always -9.80m/s

2 b. The object changes velocity, it must have an acceleration

2-7

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide50

Important concepts from video

y velocity at the top – 0m/sDisplacement at the bottom – 0m

Acceleration – always -9.80m/s2

2-7

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Truck and Soccer Ball

Slide51

A cat is dropped off a cliff that is 145 m tall.What is his acceleration?What is his initial velocity?

What is his final velocity?How long is he in the air?

Did he land on his feet?

S-4

Slide52

Practice

2-7

Slide53

A really large mouse sees a cat 100 m away. If he starts from rest and takes 28 s to catch the cat, what is his acceleration? Assume that the cat is moving away at a constant 20 m/s.

S-5

Slide54

Evil Ralphie is throwing sheep off a cliff. Bad Ralphie! He throws the first sheep upward at 22 m/s. He then waits 6 seconds and throws a second sheep downward. The cliff is 180 m tall and both sheep land (gently and on their feet) at the same time. What was the initial velocity of the second sheep?

S-6

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