Chapter 2. Kinematics in One Dimension In this chapter we study kinematics of motion in one dimension—motion along a straight line. Runners, drag racers, and skiers are just a few examples of motion in one dimension. Chapter Goal: To learn how to solve problems about motion in a straight line.

Chapter 2. Kinematics in One Dimension Topics: Uniform Motion Instantaneous Velocity Finding Position from Velocity Motion with Constant Acceleration Free Fall Motion on an Inclined Plane Instantaneous Acceleration

Chapter 2. Reading Quizzes

The slope at a point on a position- versus-time graph of an object is the object’s speed at that point. the object’s average velocity at that point. the object’s instantaneous velocity at that point. the object’s acceleration at that point. the distance traveled by the object to that point. Answer: C

The slope at a point on a position- versus-time graph of an object is the object’s speed at that point. the object’s average velocity at that point. the object’s instantaneous velocity at that point. the object’s acceleration at that point. the distance traveled by the object to that point. IG2.1

The area under a velocity-versus-time graph of an object is the object’s speed at that point. the object’s acceleration at that point. the distance traveled by the object. the displacement of the object. This topic was not covered in this chapter. Answer: D

The area under a velocity-versus-time graph of an object is the object’s speed at that point. the object’s acceleration at that point. the distance traveled by the object. the displacement of the object. This topic was not covered in this chapter. IG2.2

At the turning point of an object, the instantaneous velocity is zero. the acceleration is zero. both A and B are true. neither A nor B is true. This topic was not covered in this chapter. Answer: A

At the turning point of an object, the instantaneous velocity is zero. the acceleration is zero. both A and B are true. neither A nor B is true. This topic was not covered in this chapter. IG2.3

A 1-pound block and a 100-pound block are placed side by side at the top of a frictionless hill. Each is given a very light tap to begin their race to the bottom of the hill. In the absence of air resistance the 1-pound block wins the race. the 100-pound block wins the race. the two blocks end in a tie. there’s not enough information to determine which block wins the race. Answer: C

A 1-pound block and a 100-pound block are placed side by side at the top of a frictionless hill. Each is given a very light tap to begin their race to the bottom of the hill. In the absence of air resistance the 1-pound block wins the race. the 100-pound block wins the race. the two blocks end in a tie. there’s not enough information to determine which block wins the race. IG2.4

Chapter 2. Basic Content and Examples

Uniform Motion Straight-line motion in which equal displacements occur during any successive equal-time intervals is called uniform motion. For one-dimensional motion, average velocity is given by

EXAMPLE 2.1 Skating with constant velocity

EXAMPLE 2.1 Skating with constant velocity

EXAMPLE 2.1 Skating with constant velocity

EXAMPLE 2.1 Skating with constant velocity

EXAMPLE 2.1 Skating with constant velocity

EXAMPLE 2.1 Skating with constant velocity

Tactics: Interpreting position-versus-time graphs

Tactics: Interpreting position-versus-time graphs

Instantaneous Velocity Average velocity becomes a better and better approximation to the instantaneous velocity as the time interval over which the average is taken gets smaller and smaller. As Δt continues to get smaller, the average velocity vavg = Δs/Δt reaches a constant or limiting value. That is, the instantaneous velocity at time t is the average velocity during a time interval Δt centered on t, as Δt approaches zero.

EXAMPLE 2.4 Finding velocity from position graphically QUESTION:

EXAMPLE 2.4 Finding velocity from position graphically

EXAMPLE 2.4 Finding velocity from position graphically

EXAMPLE 2.4 Finding velocity from position graphically

EXAMPLE 2.4 Finding velocity from position graphically

EXAMPLE 2.4 Finding velocity from position graphically

Finding Position from Velocity If we know the initial position, si, and the instantaneous velocity, vs, as a function of time, t, then the final position is given by Or, graphically;

EXAMPLE 2.7 The displacement during a drag race QUESTION:

EXAMPLE 2.7 The displacement during a drag race

EXAMPLE 2.7 The displacement during a drag race

EXAMPLE 2.7 The displacement during a drag race

Motion with Constant Acceleration

Problem-Solving Strategy: Kinematics with constant acceleration

Problem-Solving Strategy: Kinematics with constant acceleration

Problem-Solving Strategy: Kinematics with constant acceleration

Problem-Solving Strategy: Kinematics with constant acceleration

EXAMPLE 2.14 Friday night football QUESTION:

EXAMPLE 2.14 Friday night football

EXAMPLE 2.14 Friday night football

EXAMPLE 2.14 Friday night football

EXAMPLE 2.14 Friday night football

EXAMPLE 2.14 Friday night football

EXAMPLE 2.14 Friday night football

Motion on an Inclined Plane

EXAMPLE 2.17 Skiing down an incline QUESTION:

EXAMPLE 2.17 Skiing down an incline

EXAMPLE 2.17 Skiing down an incline

EXAMPLE 2.17 Skiing down an incline

EXAMPLE 2.17 Skiing down an incline

Tactics: Interpreting graphical representations of motion

Instantaneous Acceleration The instantaneous acceleration as at a specific instant of time t is given by the derivative of the velocity

Finding Velocity from the Acceleration If we know the initial velocity, vis, and the instantaneous acceleration, as, as a function of time, t, then the final velocity is given by Or, graphically,

EXAMPLE 2.21 Finding velocity from acceleration QUESTION:

EXAMPLE 2.21 Finding velocity from acceleration

Chapter 2. Summary Slides

General Principles

General Principles

Important Concepts

Important Concepts

Applications

Applications

Chapter 2. Clicker Questions

Which position-versus-time graph represents the motion shown in the motion diagram? Answer: D

Which position-versus-time graph represents the motion shown in the motion diagram? STT2.1

Which velocity-versus-time graph goes with the position-versus-time graph on the left? Answer: C

Which velocity-versus-time graph goes with the position-versus-time graph on the left? STT2.2

Which position-versus-time graph goes with the velocity-versus-time graph at the top? The particle’s position at ti = 0 s is xi = –10 m. Answer: B

Which position-versus-time graph goes with the velocity-versus-time graph at the top? The particle’s position at ti = 0 s is xi = –10 m. STT2.3

Which velocity-versus-time graph or graphs goes with this acceleration-versus- time graph? The particle is initially moving to the right and eventually to the left. Answer: B

Which velocity-versus-time graph or graphs goes with this acceleration-versus- time graph? The particle is initially moving to the right and eventually to the left. STT2.4

The ball rolls up the ramp, then back down The ball rolls up the ramp, then back down. Which is the correct acceleration graph? Answer: D

The ball rolls up the ramp, then back down The ball rolls up the ramp, then back down. Which is the correct acceleration graph? STT2.5

Rank in order, from largest to smallest, the accelerations aA– aC at points A – C. aA > aB > aC aA > aC > aB aB > aA > aC aC > aA > aB aC > aB > aA Answer: E

Rank in order, from largest to smallest, the accelerations aA– aC at points A – C. aA > aB > aC aA > aC > aB aB > aA > aC aC > aA > aB aC > aB > aA STT2.6