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Lecture Outlines

Chapter 2

Physics, 3rd Edition

James S. Walker

Physics

•  Mechanics – Kinematics (studying just the motion)

•  One dimensional •  Two dimensional •  Three dimensional

– Dynamics (why the motion is happening? Motion in presence of force)

Chapter 2

One-Dimensional Kinematics

Units of Chapter 2

Learning outcomes •  Position, Distance, and Displacement

•  Average Speed and Velocity

•  Instantaneous Velocity

•  Acceleration

•  Motion with Constant Acceleration

•  Applications of the Equations of Motion

•  Motion of a freely Falling Objects

2-1 Position, Distance, and Displacement

In a coordinate system Before describing motion, you must set up a coordinate system – define an origin and a positive direction.

2-1 Position, Distance, and Displacement

The distance is the total length of travel;

if you drive from your house to the grocery store and back, How much distance is covered?

2-1 Position, Distance, and Displacement

Displacement is the change in position.

If you drive from your house to the grocery store and then to your friend’s house, What is your displacement and the distance you have traveled?

2-2 Average Speed and Velocity The average speed is defined as the distance traveled divided by the time the trip took:

Average speed = distance / elapsed time

What is the average speed of the red car a) 40.0 mi/h, b) more than 40.0 mi/h, c) less than 40.0 mi/h?

2-2 Average Speed and Velocity

Average velocity = displacement / elapsed time

If you return to your starting point, what is your average velocity?.

Average velocity

Average velocity =displacementelapsed time

vav =x f − xit f − ti

=ΔxΔt

SI units = ms

;

Dimension: [v] = [vav ] : LT

2-2 Average Speed and Velocity

Graphical Interpretation of Average Velocity

Plot this motion on a x-t graph.

2-2 Average Speed and Velocity

Graphical Interpretation of Average Velocity x-t graph:

2-3 Instantaneous Velocity Definition:

(2-4)

This means that we evaluate the average velocity over a shorter and shorter period of time; as that time becomes infinitesimally small, we have the instantaneous velocity.

What is the unit and dimension of the instantaneous velocity

v = Limit ofFor a very short time

displacementelapsed time

v = limΔt→0

ΔxΔt

2-3 Instantaneous Velocity This plot shows the average velocity being measured over shorter and shorter intervals. The instantaneous velocity is tangent to the x vs. t curve.

2-3 Instantaneous Velocity

Graphical Interpretation of Average and Instantaneous Velocity on the x-t plot

2-4 Acceleration: change of velocity

Average acceleration: Total change of velocity for the trip

(2-5)

What is the SI unit of acceleration?

What is the dimension of acceleration?

2-4 Acceleration

Graphical Interpretation of Average and Instantaneous Acceleration on v-t graph:

2-4 Acceleration Acceleration (increasing speed) and deceleration (decreasing speed)

What is the value of v final and v initial in each case?

What is the sign of a and v in each case?

2-4 Acceleration

Acceleration (increasing speed)

Deceleration (decreasing speed)

2-5 Motion with Constant Acceleration How the velocity changes If the acceleration is constant?

Write proper equations for the instantaneous and average velocity from the graph:

2-5 Motion with Constant Acceleration

How the velocity changes If the acceleration is constant?

(2-7)

Average velocity:

2-5 Motion with Constant Acceleration

Average velocity:

(2-9)

Position as a function of time:

(2-10)

(2-11)

Velocity as a function of position:

(2-12)

2-5 Motion with Constant Acceleration

The relationship between position and time follows a characteristic curve.

2-5 Motion with Constant Acceleration

2-6 Applications of the Equations of Motion Hit the Brakes!

2-7 Freely Falling Objects

Free fall is the motion of an object subject only to the influence of gravity. The acceleration due to gravity is a constant, g.

2-7 Freely Falling Objects

An object falling in air is subject to air resistance (and therefore is not freely falling).

Your key chain falling from the bridge

•  Calculate acceleration, position, and velocity of your key chain free falling from the Golden Gate Bridge (227 m) after 1,2,3,4 seconds.

•  How long it takes for the object to reach the water level?

•  What is the velocity when it hits the water. •  How much velocity is gained per second? •  How much distance is traveled per second? •  Plot the a vs. t, v vs. t, and y vs. t •  What is the conclusion?

2-7 Freely Falling Objects

Free fall from rest:

2-7 Freely Falling Objects Trajectory of a projectile:

Summary of Chapter 2

•  Distance: total length of travel

•  Displacement: change in position

•  Average speed: distance / time

•  Average velocity: displacement / time

•  Instantaneous velocity: average velocity measured over an infinitesimally small time

Summary of Chapter 2 •  Instantaneous acceleration: average acceleration measured over an infinitesimally small time

•  Average acceleration: change in velocity divided by change in time

•  Deceleration: velocity and acceleration have opposite signs

•  Constant acceleration: equations of motion relate position, velocity, acceleration, and time

•  Freely falling objects: constant acceleration g = 9.81 m/s2