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General Physics Quarter 1 | 1st Semester | 2023 Accuracy and Precision Vector Accuracy - Quantity that has both quantity and - Refers to how close a measurement is to the d...

General Physics Quarter 1 | 1st Semester | 2023 Accuracy and Precision Vector Accuracy - Quantity that has both quantity and - Refers to how close a measurement is to the direction true or accepted value - Important in the study of motion - Degree of closeness between a Examples measurement and true vale Force Precision Velocity - How close measurements of the same item Acceleration are to each other Momentum - Independent of accuracy Vector Addition / Resolution Systematic and Random Errors Vector Addition Systematic Error - The operation of adding two or more - Deviates from the true value of vectors into a vector sum measurement by a fixed amount - Vector sum is obtained by placing them - Remains constant or changes in a regular head to tail and drawing the vector from the fashion in repeated measurements in some free tail to the free head quantities Methods for Solving Vector Addition - Caused by flaw in experimental design 1. Graphical Method Random Error Drawing vectors on a graph and - Varies and is likely to be positive or negative adding them using the head-to-tail - Inconsistent and does not repeat in the method same magnitude or direction; except by chance - Caused by unpredictable variations in the readings Scientific Notation Scientific Notation - Proper format for scientific notation is a x 10ᵇ 2. Trigonometric Method - b is the power of 10 required so that the Assign them to the sides of a right scientific notation is mathematically triangle and calculate the sum as the equivalent to the original number hypotenuse of the right triangle Scalar and Vector Formulas: Distance Traveled Scalar ⅆ 𝑇 = ⅆ1 + ⅆ2 - quantity that is fully described as magnitude Resultant Vector only 𝑣1 = √𝑣12 + 𝑣22 - described by just a single number Resultant Displacement Example: Speed 𝑣1 = √𝑣12 + 𝑣22 Volume 𝑦 𝜃 = tan−1 ( ) Mass 𝑥 Time Vector Composition Formulas: Average Speed Vector Composition ⅆ - Process of compounding two or more 𝑠= 𝑡 vectors into a single resultant vector Instantaneous Speed How to Get Components of a Vector ⅆ𝑠 𝑣1 = 𝑙𝑖𝑚 𝛥𝑡→0 ⅆ𝑡 Velocity - Quantity that designates how fast and in what direction a point is moving - Rate at which an object changes position Average Velocity - Total time that an object changes position Instantaneous Velocity - The velocity of an object under motion at a Formulas: specific point in time 𝑥 = 𝑉 cos 𝜃 - Speed of an object in a particular point in 𝑦 = 𝑉 𝑠𝑖𝑛 𝜃 time with direction Formulas: Distance and Displacement Average Velocity Given Position and Time ⃗ ⅆ 𝑣(𝑡1 ) − 𝑣 (𝑡2 ) 𝑣⃗ = 𝑣𝑎𝑣𝑔 = Distance 𝑡 𝑡1 − 𝑡2 Instantaneous Velocity - Movement without direction ⅆ𝑠⃗ - Total path traveled by an object or body 𝑣⃗ = 𝑙𝑖𝑚 𝛥𝑡→0 ⅆ𝑡 Displacement - Movement with direction Acceleration - Change in position - Shortest possible straight line from the Acceleration initial point to the final point - Change in velocity over time Formulas: - Acceleration means the speed is changing, Distance but not always ⅆ 𝑇 = ⅆ1 + ⅆ2 Instantaneous Acceleration Displacement (Parallel) - Acceleration at any specific time during the ⅆ⃗ = ⅆ1 + ⅆ2 motion Displacement (Perpendicular) ⅆ 2 = √𝑣12 + 𝑣22 Formulas: Acceleration Given Position and Time 𝑣𝐹 − 𝑣0 𝑣 (𝑡1 ) − 𝑣 (𝑡2 ) 𝑎⃗ = 𝑎⃗ = 𝑡 𝑡1 − 𝑡2 Speed and Velocity 2 2 𝑣𝐹 − 𝑣0 𝑎⃗ = 2ⅆ Speed 𝑉𝐹2 = 𝑉02 + 2𝑎ⅆ - The rate of change of the position of an Instantaneous Velocity object in any given direction ⅆ𝑠⃗ Average Speed 𝑎⃗ = 𝑙𝑖𝑚 𝛥𝑡→0 ⅆ𝑡 - Ratio of distance to the time in which the distance was covered Instantaneous Speed - Speed of an object at a given or particular moment in time - Rate of change of the distance of an object with respect to time - Always greater than or equal to 0 Interpreting Data in a Graph Describing Motion Free Fall Displacement Free Fall - Displacement in a graph is the area covering - An object that is moving only because of the curve between velocity and time the action of gravity Areas Under Velocity vs. Time Curves - Described by Newton’s second law of motion - Downward movement under the force of gravity only - An object falling under the force of gravity Velocity - Could be negative or positive - When an object falls to the ground, it decreases velocity every -9.8m/s² - First, cut the graph into parts where each Upward = negative point ended Downward = positive - Then to get the displacement, solve for the Speed area that corresponds to the shapes that - Increases as object falls down were formed - An object at free fall increases speed every - In the example above, through cutting the 9.8m/s² graph, a rectangle and a triangle was Note: formed so you will get the area of those  Velocity of an object at its highest point: shapes. 0m/s² - The units will depend on the values on the graph Areas Under Acceleration vs. Time Curves Formulas: Constant Speed ⅆ = 𝑣𝑡 Constant Acceleration Velocity at Any Given Time 𝑣𝐹 = 𝑣𝑖 + 𝑎𝑡 2 1 ⅆ = 𝑣𝑖 𝑡 + 𝑎𝑡 2 2 1 ⅆ = [𝑣𝑖 + 𝑣𝐹 ]𝑡 2 Velocity at Any Given Position - Same concept with velocity 𝑣𝐹2 = 𝑣𝑖2 + 2𝑎ⅆ Finding Time Given the Position Kinematic Equations −𝑎 −(−𝑣𝑖 ) ± √[(−𝑣𝑖 )2 − 4 ( ) (ⅆ )] 2 Kinematic Equation 𝑡= −𝑎 2( 2 ) - Set of equations that describe the motion of an object at constant acceleration Note:  These equations are used depending on the values present on a certain problem, this is most helpful in finding the acceleration Formulas: 𝑣𝐹 = 𝑉1 + 𝑎𝑡 𝑎𝑡 2 ⅆ 𝑇 = 𝑣𝑖 𝑡 + 2 𝑣𝐹2 = 𝑣𝑖2 + 2𝑎ⅆ  Projectile Motion Notes:  Projectile always maintains a constant Projectile Motion horizontal velocity - Motion of an object, body or particle that  Projectile always experiences a constant travels in 2D that is the horizontal and vertical acceleration vertical motion  Horizontal and vertical motions of a Projectile projectile is completely independent to - Any body/object/particle that travels in a each other. Therefore, you should treat parabolic motion them separately Trajectory - Parabolic path travelled by an object or projectile A good way to practice is to look up worksheets Range on the internet! Kaya niyo po yan guys, Goodluck!! - Horizontal distance covered by an object - Ate Hannah Two Types of Projectile Motion 1. Projectile Launched Horizontally A projectile thrown parallel to the horizon (constant) Moves with a horizontal take off speed Speed only under the influence of its own weight There is no initial vertical velocity Velocity gets longer Equal changes over time Constant vertical acceleration 2. Projectile Launched at an Angle Object projected at an angle to the horizontal Motion begins with both x and y component Has no vertical and horizontal of 9.8m/s² Formula for Projectile Launched Horizontally: Horizontal Vertical ⅆ𝑥 𝑔𝑡 2 𝑣𝑥 = ⅆ𝑦 = 𝑡 2 ⅆ𝑥 = 𝑣𝑥𝑡 𝑣𝑦 = 𝑔𝑡