AP Physics

CHAPTER TWO

Motion in One Dimension

Teacher: Luiz Izola

Chapter Preview

1. Position, Velocity, Speed

2. Instantaneous Velocity and Speed

3. Acceleration

4. Motion Diagrams

5. Motion with Constant Acceleration

6. Freely Falling Objects

Learning Objectives

How to analyze one-dimensional motion related to displacement, time, speed, and velocity.

How to distinguish between accelerated and non-accelerated motion.

Introduction

Mechanics is the study of how objects move, how they respond to external forces, and how other factors, such as size, mass, mass distribution affect their motion. Kinematics, from Greek kinema, means motion. It is the study of motion and how to describe it, without regard for how the motion was caused.

Displacement

Simplest form of motion: One-dimensional

Frame of reference: In order to analyze any motion related problem, we need to have a point of reference in order to create logical assumptions.

Displacement: Length from initial position to final on a straight line. SI unit is meter

Δx = xf – xi

Read page 26, paragraphs 2,3. Explain.

Displacement and Velocity

Displacement can be positive or negative, it depends on the direction of the motion.

Velocity – Displacement divided by the time interval during the displacement occurrence.

Average Velocity = Δx / Δt, where:

Δx = change in position

Δt = change in time

Displacement and Velocity

Velocity SI unit is: meters/seconds.

Velocity can be positive or negative, depending on sign of displacement.

Time is always positive.

Average velocity is equals to the constant velocity needed to cover the given displacement in a time interval.

Practice Session

1. During a race on level ground, Andra runs with an average velocity of 6.02m/s to the east. What is Andra’s displacement after 137 seconds.

2. Let us try: Page 28: Ex. 2-1.

3. You drive 4 mi at 30 mi/h and then another 4 mi at 50 mi/h. Is your average speed for the 8 miles:

(a) > 40 mi/h (b) = 40 mi/h (c) < 40 mi/h

Velocity and Speed

Velocity is not the same as speed: Speed does not take into consideration direction.

Speedavg = total distance/total time

Slope of line is related to average velocity:

Slope = Δy / Δx, where:

Δy = Vertical coordinate change

Δx = Horizontal coordinate change

Instantaneous Velocity and Speed

Instantaneous velocity: It is the velocity at a specific time.

vx = lim Δt=>0 (Δx/ Δt) , in calculus this

change is called the derivative of x with respect to time. It is written dx/dt. Try page 30: 2-3.

To determine the instantaneous velocity, construct a straight-line tangent to the velocity graph line. The point where the lines touch is the instantaneous velocity at that specific time.

Acceleration

Acceleration is the rate of velocity change with respect to time. Average acceleration is calculated by dividing the total velocity change by the total time change.

aavg = Δv / Δt

SI acceleration units: meters / second2

Instantaneous Acceleration

Acceleration can be positive or negative like velocity. It depends on the direction.

Instantaneous acceleration is the limit of the average acceleration as the time change approaches zero.

ax = lim Δt=>0 (Δvx/ Δt) = dvx/dt

Practice Session

1. A shuttle bus slows down with an average acceleration of -1.8m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop?

Acceleration

Since acceleration is directly proportional to velocity, it has direction and magnitude. Velocity positive Acceleration positive Velocity negative Acceleration negative Velocity constant Acceleration is zero Read page 33: 2-4. Try page 33: 2-5. Read section 2.4, pages 34-35

Acceleration

A negative acceleration does not mean that speed is decreasing. It is related to direction.

When velocity and acceleration of an object have the same sign, object’s speed increases. Velocity and acceleration point to same direction.

When they have opposite signs, speed decreases. Velocity and acceleration point to opposite directions.

Motion with Constant Acceleration

If a particle moves with constant acceleration, the average acceleration is equal to the instant acceleration. Displacement depends on acceleration, initial velocity, and time.

Velocity as a function of time. (Acceleration ax

is constant)

vxf = vxi + axt

Motion with Constant Acceleration

Average Velocity Equation:

vx = ½ (vxi + vxf)

Position as a Function of Time Equations:

xf = xi + ½ (vxi + vxf)t

xf = xi + vxi t + ½axt2

Motion with Constant Acceleration

Velocity as a Function of Position Equation:

vxf2 = vxi2 + 2a(xf – xi)

This equation allows as to relate the velocity at one position to the velocity at another position.

Learn the Table 2-2, page 38.

Try Pages 38-39: 2.6, 2.7, 2.8

Freely Falling Objects

Free-fall bodies have constant acceleration.

If air resistance is disregarded, objects dropped near the surface of the planet fall with the same constant acceleration. This acceleration is due to gravity, and the motion is referred to as Free Fall.

Falling Objects

Gravity’s Acceleration: ag = 9.81 m/s2

Because an object in free fall is acted on only by

gravity, ag is also known as free-fall acceleration.

Acceleration is constant during upward and downward motion.

Let us talk about Quizzes 2.6, 2.7 0n page 41.

Practice Session

Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upward. If the volleyball starts from 2.0 m above the floor. How long it will be in the air before it strikes the floor?

Let us go through 2.9, 2.10 on page 41. Let us do 2.12 on page 43.

Homework

Page 49: #1

Page 50: #3, #5, #7, #9

Page 51: #15 , #21, #23

Page 52: #25, #27

Page 53: #43, #45, #47