DISPLACEMENT AND VELOCITY Chapter 2-1

Objectives Describe motion in terms of frame of reference, displacement, time and velocity. Calculate displacement, velocity and time interval. Interpret position vs. time graphs.

Kinematics deals with the concepts that are needed to describe motion. Dynamics deals with the effect that forces have on motion. Together, kinematics and dynamics form the branch of physics known as Mechanics.

Describing Motion: this slide is not in your notes! Are these two motions different?

2.1 Displacement As any object moves from one position to another, the length of the straight line drawn from its initial position to the object’s final position is called displacement.displacement Displacement is the change in position of an object. Displacement doesn’t always tell you distance an object moved.  Displacement = final position – initial position  ∆x = x f -x o ∆x = x f -x  Si units – meters (m)

2.1 Displacement Displacement is not always equal to the distance traveled.  Displacement can be positive or negative. If displacement is positive, the object moves to the right. If the displacement is negative, the object moves to the left.

2.1 Displacement

2.2 Speed and Velocity Average speed is the distance traveled divided by the time required to cover the distance. SI units for speed: meters per second (m/s)

2.2 Speed and Velocity Average velocity is the displacement divided by the elapsed time. SI units for velocity: meters per second (m/s)

2.2 Speed and Velocity Velocity gives both direction and magnitude (amount) while speed only gives the magnitude - no direction  Average velocity does not tell you the speed or velocity of the moving object at each moment or instant. Average velocity can be positive or negative depending on direction moved. Time can never be negative!

Average Velocity: The slope of a position vs. time graph is called the average velocity.  ‘Should get something similar to this from your lab data’

Average Velocity The definition of average velocity holds even if the slope changes. This would be the slope of the line connected the final and initial points.

Average Velocity: Steeper slope means a faster moving object.

Speed and velocity: Velocity and speed can be used interchangeably in everyday language  In Physics, however, there is a distinction: Speed is a Scalar quantity (numerical value = magnitude only) Velocity is Vector quantity - Describes motion with both direction and a numerical value (magnitude and direction)

Constant Velocity Model: Velocity vs. Time Graph With constant velocity, On a graph of velocity vs. time, displacement can be calculated by finding the area under the graph. If the velocity is negative, the displacement calculate will be negative.

Constant Velocity Model: Velocity vs. Time Example Use the graph to calculate the displacement of the object:  From 0 s to 3 s  From 3 s to 6 s  From 6 s to 9 s  From 0 s to 9 s

Velocity vs. Time Practice Use the graph to calculate the displacement of the object:  From 0 s to 2 s  From 2 s to 4 s  From 4 s to 7 s  From 7 s to 9 s

Practice problem example:- The ‘GUESS’ method If Joe rides his bicycle in a straight line for 15 sec with an average velocity of 12.5 m/s south, how far has he ridden? Given: t = 15 sec, v = 12.5m/s Unknown: D = ? Equation and model: v = D/t (kimenatics) Separate the unknown: D= v.t Substitute and solve: D= 12.5m/s x 15s 187.5m Does the answer make sense? Yes!!

More practice:- ‘GUESS’ method

More Practice Problems 1.What distance will a car traveling 65 km/hr travel in 3.0 hrs? 2.What distance will be traveled if you are going 120km/hr for 30. min? 3.How long will it take to go150 km traveling at 50 km/hr? 4.How long will it take to travel 200 km traveling 100 m/s? 5.If a rocket travels km in 3.00 hours, what is its speed? 6.A car travels 240 km in 2.0 hrs and a sprinter travels a 100. m in 9.5 s. Which is traveling faster and by how much?

CLASS ASSIGNMENT / HOMEWORK I will not accept late work

Acceleration Section 3

(REVIEW) Displacement for constant acceleration The displacement from time 0 to time t is the area under the velocity graph from 0 to t. Area = ½ b h t (s) v (m/s)

(REVIEW) Displacement for constant acceleration If we don’t know v, we can calculate it from a. Area =l w + ½ b h t (s) v (m/s)

Instantaneous Velocity – write this under your instantaneous acceleration paragraph The instantaneous velocity indicates how fast the car moves and the direction of motion at each instant of time.

Changes in velocity: The direction of acceleration depends on the direction of the motion and on whether the velocity is increasing or decreasing

2.3 Acceleration The notion of acceleration emerges when a change in velocity is combined with the time during which the change occurs. Acceleration is the measure of how fast something speeds up or slows down

2.3 Acceleration DEFINITION OF AVERAGE ACCELERATION SI units for acceleration: (m/s 2 )

2.3 Acceleration Example 3: Acceleration and Increasing Velocity Determine the average acceleration of the plane. G: U: E: (kinematics ) S:

2.3 Acceleration

2.3 Acceleration Example 3: Acceleration and decreasing Velocity Calculate the average acceleration G: U: E: (kinematics ) S:

2.3 Acceleration

Graph for speeding up motion – Acceleration describe the following motion Everyday examples of such motion include: Driving a car Throwing a ball Kids sliding at the playground

Changes in velocity: Instantaneous acceleration:  Since in some situations, the acceleration of an object can be constant, as a result, it will be the same value at any instant of time.  The plus or minus sign before the number indicates the two possible directions for the acceleration vector when the motion is along a straight line.

Interpret The Graph Below: Distance vs. time The graph shows __________

Interpret The Graph Below: Distance vs. Time (constant velocity) : The object is __________

Interpret The Graph Below: Distance vs. Time ( constant negative velocity) This object is ________________

Interpret The Graph Below: Distance vs. Time (acceleration) The curve in the graph shows that _______________

Interpret The Graph Below: Distance vs. Time (deceleration) The curve in the graph shows that the objects _______________

Interpret The Graph Below: Distance vs. Time In the first part of the graph the object is ____________ In the second part of the graph the object is _______________ In the third part the object is ___________

Interpret The Graph Below:: Velocity vs. Time (constant velocity) The objects is _______

Interpret The Graph Below:: Velocity vs. Time The objects is _______

Interpret The Graph Below: Velocity vs. Time (constant acceleration) The objects velocity is ______________ this is known as ____________ The straight line shows that the object is moving at a _____________

Interpret The Graph Below: Velocity vs. Time The objects velocity is _________________ The straight line shows that _______________

Interpret The Graph Below: Velocity vs. Time The objects velocity is _________________

Interpret The Graph Below: Velocity vs. Time The objects velocity is _________________

2.4 Equations of Kinematics for Constant Acceleration For one dimensional motion it is customary to dispense with the use of boldface symbols overdrawn with arrows for the displacement, velocity, and acceleration vectors. We will, however, continue to convey the directions with a plus or minus sign.

2.4 Equations of Kinematics for Constant Acceleration Let the object be at the origin when the clock starts.

2.4 Equations of Kinematics for Constant Acceleration

Equations of Kinematics for Constant Acceleration

2.4 Equations of Kinematics for Constant Acceleration G: U: E: (kinematics ) S:

2.4 Equations of Kinematics for Constant Acceleration Example 6 Catapulting a Jet Find its displacement.

2.4 Equations of Kinematics for Constant Acceleration G: U: E: (kinematics ) S:

Practice 2C A jet plane lands with a speed of 100 m/s and can accelerate uniformly at a maximum rate of -5.0 m/s 2 as it comes to rest. Can this airplane land at an airport where the runway is 0.80 km long?

Practice 2C, p. 53 #3 Constant Acceleration

CLASS ASSIGNMENT / HOMEWORK I will not accept late work

Chapter 2 Section 6: Falling Objects

Free Fall acceleration: An object thrown or dropped in the presence of Earth’s gravity experiences a constant acceleration directed toward the center of the earth. This acceleration is called the free- fall acceleration, or the acceleration due to gravity.  Free fall acceleration is the same for all objects, regardless of their mass.

Free fall acceleration: The value for free fall acceleration used in this book is:  g = 9.81 m/s 2. In this book, the direction of the free fall acceleration is considered to be negative because the object accelerates toward earth. Negative Positive

2.6 Freely Falling Bodies

Free fall acceleration: Since gravity on earth is constant at 9.81m/s 2,  If 2 objects of different masses are dropped from the same height, they will both hit the ground at the same time considering no air resistance. No matter what their masses are. If there is air resistance, some objects may be slowed down The more surface area an object has, the more air resistance it will experience.  ex. A wadded piece of paper will fall faster than a flat piece of paper which will experience more air resistance due to its larger surface area

An apple and a feather falling at the same rate absent air resistance (vacuum)

Free fall acceleration: Describe the acceleration of the object as it falls off the cliff – notice the change in velocity after each second of fall

Free fall acceleration: All objects, when thrown up will continue to move upward for some time, stop momentarily at the peak, and then change direction and begin to fall. Velocity at the top of the arc is 0 m/s

What goes up must come down!! In an upward displacement of an object, as soon as the ball is released with an initial positive velocity, it has an acceleration of -9.81m/s 2, causing the object to slow down until it stops momentarily. It then changes direction moving downward with an increasing velocity.

Distance vs. Time and Velocity vs. time graph of an object thrown up in the presence of gravity

2.6 Freely Falling Bodies Example 10 A Falling Stone A stone is dropped from the top of a tall building. After 3.00s of free fall, what is the displacement, y, of the stone?

Example 10: A falling stone 2.6 Freely Falling Bodies

2.6 Freely Falling Bodies Example 12 How High Does it Go? The referee tosses the coin up with an initial speed of 5.00m/s. In the absence of air resistance, how high does the coin go above its point of release?

Example 12: How high does it go? 2.6 Freely Falling Bodies

2.6 Freely Falling Bodies Conceptual Example 15 Taking Advantage of Symmetry Does the pellet in part b strike the ground beneath the cliff with a smaller, greater, or the same speed as the pellet in part a?

2.7 Graphical Analysis of Velocity and Acceleration

CLASS ASSIGNMENT / HOMEWORK I will not accept late work

position x as a function of time t Average velocity : (slope of the line) xx tt x1x1 x2x2 t1t1 t2t2 t x Displacement :