Physics 20 - Unit 1.docx

Unit 1 - Kinematics (Motion) Lesson 2011 - Language of Motion Necessary Foundations [Significant Digits (Sig Digs)] - indicates accuracy of a measurement - - - - - [Scientific Notation] - expresses very large or very small numbers (*a* x 10*^n^*) Large Numbers - Moving decimal place...

Unit 1 - Kinematics (Motion) Lesson 2011 - Language of Motion Necessary Foundations [Significant Digits (Sig Digs)] - indicates accuracy of a measurement - - - - - [Scientific Notation] - expresses very large or very small numbers (*a* x 10*^n^*) Large Numbers - Moving decimal places to the left, positive exponent - Example: 4,500,000 = 4.5 x 10^6^, indicates you multiply 4.5 by 6 (6 decimal places to the left) Small Numbers - Moving decimal places to the right, negative exponent - Example: 0.00032 = 3.2 x 10^-4^, indicates you divide 3.2 times 0 4 times (4 decimals to the right) [Calculating with Sig Digs] - calculated answers with extra sig digs are rounded back Adding/Subtracting - round answer to the same precision (decimal places) as the least precise value - Example: 11.2 + 0.24 + 0.336 = 11.776 - rounded to 11.8 (one decimal) Multiplying/Dividing - value with least sig digs determines \# of sig digs in answer - Example: (34.28)/(4.8) = 7.141666 - rounded to 7.1 (2 sig digs) 2011 Objectives 1. 2. 3. 4. 5. 6. 7. Kinematics [Definition] - Science of the motion of objects to develop mental models which describe object motion without concern for forces, masses or energy Vectors and Scalars [Scalar Quantity] - a magnitude, possibly with units like length (m) or weight (kg) Examples: speed of 80km/h, mass of 99 kg, distance of 1200m, time of 23 minutes [Vector Quantity] - has a magnitude (size, amount), unit and direction (left, North, down) Examples: velocity of 120km/h \[North\], displacement of 45m \[down\] [Uses of Vectors] - giving directions, reporting wind conditions, planning aircraft flights, aiming rockets into space Vector Diagrams A vector is represented on paper by an arrow → The tail of the arrow shows the starting point, the arrowhead shows the direction and endpoint The length of the arrow line shows the magnitude drawn to scale Displacement Equations **Δd** - displacement, change in position of the object **Δt** - interval of time → - vector notation When writing displacement by hand, the vector notation is included over the letter "d", the direction may also be given after the unit, in square brackets. [Calculating Displacement ] To calculate displacement you need to subtract the initial position, *d*~i~, from the final position, *d*~f~. Therefore, Δ*d* = *d*~f~ - *d*~i~ Note: Subtracting a vector is the same as adding it's opposite, so a negative west direction would be the same as a positive east direction Example: 10m \[E\] - 5m \[W\] = 10m \[E\] + 5m \[E\], both = 15m \[E\] [Final Position Equation] - *d*~f~ = *d*~i~ + Δ*d* [Starting Position Equation] - *d*~i~ = *d*~f~ - Δ*d* Speed and Velocity Speed is a scalar and does not keep track of direction, velocity is a vector and is direction-aware. [Average Velocity] V~av~ = change in position/change in time V~av~ = displacement/change in time V~av~ = Δ*d*/Δ*t* Example: A car travels east for 2.0 hours and travels 220km in that time, average velocity? V~av~ = Δ*d*/Δ*t =* 220km \[East\]/2.0h = 110km/h\[East\] [Average Speed] s = distance travelled/time taken s = d/t Example: If a car travels 100km in 2 hr, d/t = 100km/2h = 50km/h Graphing Vectors Motion in one dimension involves vectors that are collinear, lie along the same straight line When more than one vector describes motion, you need to add the vectors. You can add and subtract vectors graphically as well as algebraically, given they represent the same quantity or measurement. [Adding Vectors] - You can determine the sum of all vector displacements graphically by adding them up tip to tail, the sum of this series is called the resultant vector.  [Subtracting Vectors] - You can find the displacement by using the equation Δ*d = d~2~ - d~1~* or create a new reverse direction vector where Δ*d* starts at the tip of *d~1~* and ends at the tip of *d~2~* Definitions [Magnitude] - A measure of the size of a quantity [Scalar] - Quantity that has magnitude but no direction [Vector] - Quantity that has magnitude and direction [Displacement] - The difference between the initial position of something and any later position, a vector quantity [Distance] - How much ground an object covered during it's motion, a scalar quantity [Speed] - distance travelled per unit of time [Velocity] - rate of change of position in relation to time [Δ(Delta)] - "change in" Lesson 2012 - Position-Time Graphs 2012 Objectives 1. Position-Time Graphs - - - Position-Time Velocity Velocity is the [slope] of a displacement-time or position-time graph → Slope = rise/run = change in position/change in time [Finding Velocity (positive slope):]  1. 2. 3. Example: [Finding Velocity (negative slope):] 1. Example:  Frame of Reference - - Converging and Diverging [Coverging Lines] - objects are approaching each other [Diverging Lines] - objects are moving apart from each other [Line Intersection] - both objects have the same position, meet at this point Relative Velocity When two objects are moving in [opposite directions], (towards each other) their combined speed is the sum of both velocities Ex: 2.0m/s + 0.6667m/s = 2.6667m/s When two objects are moving in the [same direction] the relative velocity is the difference between both velocities Ex: 2.25m/s - 2.0m/s = 0.25m/s Curved Line Graphs [Positive Direction Lines] - moving forward, away from reference point [Negative Direction Lines] - moving backward, toward/in other direction of reference point [Flat Horizontal Line] - at rest, no movement [Straight Lines] - uniform (constant) velocity [Curved Line] - changing (non-constant) velocity, steeper line = faster [Finding Average Velocity (curved lines):] 1. 2. 3. Ex: Δd = (1600 - 0) / Δt = (520 - 0) V = 3.0769 = 3.08  [Finding Average Speed (curved lines):] In some cases, like when the start and end point are both 0, it may be better to find the average speed rather than the average velocity. To do this: 1. 2. 3. Displacement, Velocity and Time [Velocity] = d / t [Time] = d / v [Displacement] = v x t Definitions [One-Dimensional Motion] - motion in a straight line [Slope] - measure of the steepness of a curve, represents velocity on a position-time graph [Uniform Motion] - motion at constant speed in a straight line Lesson 2013 - Velocity-Time Graphs 2013 Objectives 1. 2. 3. 4. 5. Velocity-Time Graph Graph showing velocity of an object at varying times, velocity = y-axis; time = x-axis Positive velocity - Moving forward Negative velocity - Moving in the opposite direction Constant Velocity - Flat line Velocity-Time Graph vs. Position-Time Graph [Constant Zero Velocity] - Object is not moving - Appears as a flat line at 0 on both velocity-time and position-time graph [Positive Velocity] - Object moving in a positive direction - Flat line above zero on velocity-time graph; upwards on position-time graph [Negative Velocity] - Object moving in negative direction (backwards) - Flat line below zero on velocity-time graph; downwards on position-time graph Constant Zero Positive Negative  Ticker Tape Diagram - Distance constant between points - constant speed, uniform acceleration Distance increasing between points - speeding up, accelerating Distance decreasing between points - slowing down, decelerating Acceleration Shows a change in velocity in a unit of time [(m/s\^2)] [Uniform Acceleration] - object changes velocity by the same amount through each unit of time Velocity-Time Graph - Slope = change in velocity/change in time (rise/run) Positive slope - positive acceleration Negative slope - negative acceleration, velocity changes direction Instantaneous Velocity/Acceleration [Instantaneous Velocity] - Given by the slope of the tangent to a position-time graph; rate of change of an object\'s position; specific to a given point [Instantaneous Acceleration] - Given by the slope of the tangent to a velocity-time graph; rate of change of an object\'s position; specific to a given point Used for non-uniform change (curved lines) Uniform motion - Objects average velocity/acceleration and instantaneous velocity/acceleration are the same Acceleration - Velocity - - - - \* When the sign of velocity and acceleration are the same - speed is increasing \* \* When the sign of velocity and acceleration are opposites - speed is decreasing \*