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Slide1

Describing Motion: Kinematics in One Dimension

AP Physics

Chapter 2

Slide2Describing Motion: Kinematics in One Dimension

AP Physics

Section 2-1 Reference Frames and Displacement

Slide3Describing 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

Slide4Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Mechanics â study of

motion, force, energy

Kinematics â how objects move

Dynamics â why objects move

Translational Motion â move without rotation

2-1

Slide5Reference Frames (Frames of Reference)Are we moving?Compared to what?Usually with ârespect to the Earthâ

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

Slide6Positive â up and rightNegative â down and left

2-1

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide7Defining Motion

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

Displacement â 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

Slide8Distance vs. Displacement

2-1

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide9Distance â scalar (magnitude)Displacement â 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

Slide10AP PhysicsSection 2-2 Average Velocity

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide112-1

Distance Time Graph Gizmo

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide12Average Speed â distance per unit time (scalar)

Average Velocity â 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

Slide132-2

Distance Time Velocity Graph Gizmo

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide14AP PhysicsSection 2-3 Instantaneous Velocity

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide15Instantaneous Velocity â 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

Slide16Slope 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

Slide17Using the graph calculate the average velocity between t0

=2 and t=5APP-Matt-09

S-2

Slide18Average Acceleration â 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

Slide19AP PhysicsSection 2-4 Acceleration

Describing Motion: Kinematics in One Dimension

understand the general relationships among position, velocity, and acceleration

Slide20Acceleration 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

Slide21AP PhysicsSection 2-5 Motion at Constant Acceleration

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide22Describing Motion: Kinematics in One Dimension

IA1b -

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

2-4

Slide23Describing 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 â you will use them a lot

2-5

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide24Describing 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

Slide25Describing 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

Slide26Describing 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

Slide27Now we combine the last three equations

2-5

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide28For 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

Slide29Combine with our average velocity definition

2-5

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide30Describing Motion: Kinematics in One Dimension

Solve the definition of acceleration for time

2-5

Slide31Describing Motion: Kinematics in One Dimension

Combine and you get

2-5

Slide32Finally, solve for final velocity

2-5

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide33The 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

Slide34AP PhysicsSection 2-6 Solving Problems

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide35Determine 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 âThe Physicsâ 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

Slide36Make 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

Slide37A 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 â car

Diagram

2-6

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide38A 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 â 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

Slide39A 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 â car is going through negative acceleration in 1D, acceleration is constant

Equation â 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

Slide40A 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 â car is going through negative acceleration in 1D, acceleration is constant

Equation â 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

Slide41A car is behind a truck going 25m/s on the highway. The carâs 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

Slide42Object â 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 â 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

Slide435. Time for car to pass

2-6

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide44Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

5. How far did the car travel?

Â

Slide455. 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 âboom?â

Slide46A 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

Slide47AP PhysicsSection 2-7 Falling Objects

Describing Motion: Kinematics in One Dimension

understand the special case of motion with constant acceleration

Slide48We will ignore air frictionWe will learn the why later.Acceleration due to gravity at Earthâs 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

Slide49Two common misconceptionAcceleration and velocity are always in the same direction a. No, as an object is thrown upward, velocity is +y, acceleration is ây

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

Slide50Important concepts from video

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

Acceleration â 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

Slide51A 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

Slide52Practice

2-7

Slide53A 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

Slide54Evil 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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