Physics I Honors Good morning You measure your new yard with a meter stick so that the dimensions are 20m±3cm by 30 meters±6cm. How do you make sure you will not be short ordering the perimeter fencing and the square meters of sod?

Physics I Honors Good morning part II You live on a square block 500m each side. You jog 3 times around the block. What distance did you run? What was your displacement? You travel 30m east then 40m south. What was your displacement?

Physics I Honors Kinematics I - Velocity Position and Distance

Physics I Honors Kinematics Is the study of motion without regard for the forces causing the motion or … the description of motion using: Position (s) –The location of an object in space –changes in position can be described by distance or displacement V elocity (v) –how fast an object is changing its position Acceleration (a) –how fast the velocity of an object is changing

Physics I Honors Position vs Distance Position –Must be defined relative to a reference point. –Must be defined using both magnitude and direction. –Position (s) is the location of an object in space –units: m, cm, km Distance –Distance is the separation between any two points. –It is a scalar quantity, defined only by magnitude.

Physics I Honors What is a Scalar? A scalar is a quantity that is described only by magnitude…such as distance. –it may have units e.g. kg (it may not) –it does not have any direction –it may have a sign +ve or -ve –it may be real, or integer –The distance from Jacksonville to Baldwin is 10 kilometers.

Physics I Honors Displacement A objects displacement is defined as the separation between an object and a reference point. It is a vector quantity, defined by magnitude and direction. Displacement is the change in position of an object (d = s f - s i ) sisi sfsf d = s f – s i displacement = d d

Physics I Honors What Is a Vector? A vector is a quantity that must be described by magnitude and direction. Magnitude –Size or quantity in unit of measurement –10 meters, 5 Newtons Direction –Compass direction: North, Southeast –Angle: 25 o from the positive x axis

Physics I Honors Vector –an arrow drawn to scale used to represent a vector quantity –vector notation

Physics I Honors End of day 3

Physics I Honors Graphical (Tip-to-Tail ) Method Example 1: Add these vectors using the tip-to-tail method. +

Physics I Honors Graphical (Tip-to-Tail) Method += Is the resultant

Physics I Honors What is a Resultant?

Physics I Honors How does one solve for displacement? d = s f – s i d = (x 1,y 1 ) – (x 2,y 2 )How do you do this? Realize that displacement is a vector so you must decide to use either the Cartesian or polar coordinates d s i = (x i,y i ) s f = (x f,y f ) d = s f – s i X Y

Physics I Honors Describing Vectors Cartesian Coordinates (d x,d y ) d x = x 2 – x 1 = distance in the x-direction d y = y 2 – y 1 = distance in the y-direction Polar Coordinates (d,  ) “How far and in which direction”  = measured directly from graph

Physics I Honors Describing Distance leg 1 = 2 miles leg 3 = 2 miles leg 2 = 3 miles N Total DISTANCE Traveled = 2 miles + 3 miles + 2 miles = 7 miles

Physics I Honors Describing Displacement N displacement vector Describing Displacement First Method (Cartesian) 3 miles East 4 miles North (3, 4) miles put ‘horizontal’ coordinate 1st put ‘vertical’ coordinate 2nd

Physics I Honors Displacement Magnitude N displacement vector 3 miles 4 miles Second Method (Polar) 1st - calculate length of displacement vector

Physics I Honors Displacement Direction N displacement vector  3 miles 4 miles 2nd – Calculate the angle using trigonometric relationships

Physics I Honors Displacement Vector (Polar Notation) Describe the displacement vector by its length and direction N displacement vector  3 miles 4 miles

Physics I Honors Kinematics I - Velocity Graphing

Physics I Honors Objectives for Graphing Measure, graph, analyze, and interpret laboratory data. Identify the relationships that may exist between variables (direct, inverse, and quadratic) and the graph shapes, which indicate these relationships (straight line, hyperbola, and parabola).

Physics I Honors GRAPHING Graphing is the pictorial relationship between quantities –coordinate = any point w/in a graph. –Slope =  rise /  run or  y /  x  = means change x = horizontal axis y = vertical axis

Physics I Honors All relationships involve only two variables. The Independent Variable – –this is the variable that you control or manipulate. –It is almost always plotted on the X-axis. The Dependent Variable – –this is the variable that responds to the independent variable. –It is usually plotted in the Y-axis.

Physics I Honors Graphical Analysis Graphical analysis provides a tangible representation of a relationship from which you can make predictions and inferences. –Mass of a substance vs. volume –Speed of a car vs. braking distance –Amount of light vs. plant growth

Physics I Honors What are the rules? The graph has a title… The scale of the graph is determined by the range of the data and does not need to start at 0,0 The independent variable is plotted on the x-axis The dependent variable is plotted on the y-axis All variables have names and units You construct a best fit line through the points

Physics I Honors Linear Relationships The dependent variable varies directly with the independent variable. Plot is a straight line. y  x or y = kx y = mx + b

Physics I Honors Parabolic (Exponential) Relationship The dependent variable varies with the square of the independent variable. y  x 2 or y = kx 2 Plot does not appear as a straight line. Note that one variable changes faster than the other resulting in a curved line.

Physics I Honors Inverse (Hyperbolic) Relationships The dependent variable varies in the opposite direction of the independent variable. As x goes up, y goes down. y  1/x or y = k/x This results in a line that starts high and ends low. It can be straight or curved.

Physics I Honors Graphical Analysis

Physics I Honors Slope expresses the relationship between the variables. How y is changing as x is manipulated. M =  Y/  X  Y = Y 2 -Y 1  X = X 2 -X 1 The units of the slope define the meaning of the slope.

Physics I Honors Area Under the Curve The shaded area is the area under the curve. You determine the area by adding up the areas of each triangle and square. Again, the units of this calculation, define what the number represents.

Physics I Honors Interpolation and Extrapolation Interpolation is the reading or analysis (inference or prediction) of the graph from within the plotted data points. Extrapolation is the reading or analysis (inference or prediction) of the graph from outside of the plotted data points. This can lead to a significant source of error.

Physics I Honors Kinematics I - Velocity Position-Time Graphs

Physics I Honors Graphing the Relationships Between s, v, & a s is the position v is the rate of change of s with time a is the rate of change of v with time consider a graph of s vs. time –s on vertical axis –time on horizontal axis –rate of change is interpreted as the slope

Physics I Honors Good morning III What is the position time characteristic for uniform motion, i.e. constant velocity What will it plot as? What is the slope???

Physics I Honors Position – Time for Constant Velocity

Physics I Honors Position – Time for Constant Velocity

Physics I Honors Position – Time for Acceleration

Physics I Honors Slope of Position-Time is Velocity

Physics I Honors Changes in the slope quick change –very steep slope positive slope –up and to the right negative slope –down and to the right slow change –very flat slope

Physics I Honors Slope Practice 1 Calculate the velocity of the object whose graph is shown above. -24m/8s = -3 m/s

Physics I Honors Slope Practice 2 Determine the velocity of the object whose motion is graphed at the left. 20m/5s = 4 m/s

Physics I Honors example Text page 52, #46,47

Physics I Honors Kinematics I - Velocity Speed Vs Velocity

Physics I Honors Speed A scalar quantity referring to how fast an object is moving.scalar quantity –A fast-moving object has a high speed while a slow-moving object has a low speed. –An object with no movement at all has a zero speed. The distance traveled per unit time. It units are meters per second (m/s).

Physics I Honors Velocity Velocity is a vector quantity describing displacement per unit time. Its units are meters per second (m/s). It is defined relative to a reference point. Velocity describes both speed and direction. Depending on your direction, it can be negative or positive.

Physics I Honors Average Speed Total distance divided by total time of travel; Rate you would have to travel constantly to cover the same distance in the same time

Physics I Honors Average Velocity Total displacement divided by total time of travel; Rate you would have to travel constantly to cover the same displacement in the same time

Physics I Honors Kinematics I - Velocity Instantaneous Velocity

Physics I Honors Average and Instantaneous instantaneous speed – speed at any given instant in time; speedometer reading, for example instantaneous velocity - specifies how fast and in what direction one is moving at one particular point in time magnitude of instantaneous velocity is exactly the same as instantaneous speed

Physics I Honors From a Graph Instantaneous Velocity –the slope of the displacement versus time graph –Determine the average velocity –Take average between smaller and smaller intervals –Until you get to the tangent line –The slope of the tangent line is the instantaneous velocity at that point in time

Physics I Honors Kinematics I - Velocity Problem Solution

Physics I Honors Problem Solution Guidelines Draw a sketch –Indicate origin and positive direction List the given quantities using the symbols of the equations. (d i, v i, a) Identify the unknown Write the general equation of kinematics you will be using, i.e.

Physics I Honors More Guidelines Isolate the unknown. Rewrite the isolated equation using the known quantities. Check your units Make sure you are answering the question asked. –Your answer may be perfectly correct for the wrong question.

Physics I Honors Kinematics I - Velocity Velocity-Time Graphs

Physics I Honors Velocity – Time for Constant Velocity

Physics I Honors Velocity – Time for Constant Acceleration Time (s) Velocity(m/ s)

Physics I Honors Velocity – Time for Zero Acceleration Time (s) Velocity(m /s)

Physics I Honors Area Under Velocity-Time Graph The shaded area is representative of the distance traveled by the object during the time interval from 0 seconds to 6 seconds.

Physics I Honors Area Under Velocity-Time Graph The shaded area is representative of the distance traveled by the object during the time interval from 0 seconds to 4 seconds.

Physics I Honors Area Under Velocity-Time Graph The shaded area is representative of the distance traveled by the object during the time interval from 2 seconds to 5 seconds.

Physics I Honors Constant Positive Velocity

Physics I Honors Constant Negative Velocity

Physics I Honors Positive Velocity Positive Acceleration

Physics I Honors Positive Velocity Negative Acceleration

Physics I Honors Negative Velocity Negative Acceleration

Physics I Honors Negative Velocity Positive Acceleration

Physics I Honors Speeding Up & Slowing Down Negative acceleration can mean speeding up or slowing down. The same is true with positive acceleration.

Physics I Honors Passing Lane – Position-Time

Physics I Honors Passing Lane – Velocity-Time

Physics I Honors Vector Addition in One Dimension

Physics I Honors homework Motion hand out Text page 55 do multiple choice practice test Visit physicspp.com