NU MOA General Physics 1 Motion Graphs PDF

General Physics 1 Review of Concepts  What is Acceleration? Acceleration is the rate of change in the velocity. To calculate acceleration, you use the following formula: 𝛥𝑣 v – v0 Acceleration (a) = 𝑐ℎ...

General Physics 1 Review of Concepts  What is Acceleration? Acceleration is the rate of change in the velocity. To calculate acceleration, you use the following formula: 𝛥𝑣 v – v0 Acceleration (a) = 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡𝑖𝑚𝑒 = 𝛥𝑡 = t – t0 Standard Unit: meters per second squared (m/s2 )  Speeding Up & Slowing Down If the acceleration is in the If the speed decreases, the same direction as the velocity, acceleration is in the opposite speed increases and direction from the velocity, then acceleration is positive acceleration is negative. An object accelerates when there’s a change in velocity. v v Car speeds up a v v Car slows down a  An object accelerates when there’s a change in its direction or it changes both velocity and direction. v a  Acceleration The acceleration is proportional to the magnitude of the force. The direction of acceleration is same as direction of force. Pulling the wagon with twice the force produces twice the acceleration and acceleration is in direction of force.  Acceleration & Velocity As velocity increases, so does acceleration As velocity decreases, so does acceleration When direction changes, so does acceleration When there is a constant velocity, there is no acceleration  Checkpoint! What happens to the What is the acceleration when we relationship of What law explains double the mass and acceleration with this relationship apply the same force? force? between directly proportional acceleration, Acceleration decreases mass, and force? What happens to the What is the acceleration if we relationship of Newton’s 2nd Law quadruple the force acceleration with of Motion: applied? mass? The Law of Acceleration is quadrupled inversely proportional Acceleration Average acceleration Average Acceleration v v f − vi Note: we are plotting aavg = = t t f − ti velocity vs. time Velocity as a function of time v f (t ) = vi + aavg t It is tempting to call a negative acceleration a “deceleration,” but note: When the sign of the velocity and the acceleration are the same (either positive or negative), then the speed is increasing When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing Average acceleration is the slope of the line connecting the initial and final velocities on a velocity-time graph  Instantaneous & Uniform Acceleration The limit of the average acceleration as the time interval goes to zero v dv d dx d v 2 a = lim = = = t →0 t dt dt dt dt 2 When the instantaneous accelerations are always the same, the acceleration will be uniform. The instantaneous acceleration will be equal to the average acceleration Instantaneous acceleration is the slope of the tangent to the curve of the velocity-time graph.  Learning Objectives  Learning Targets: 1. Describe motion; 2. Convert a verbal description of physical situation involving uniform acceleration in one dimension into mathematical description; 3. Recognize whether or not a physical situation involves constant velocity or constant acceleration; and 4. Interpret and construct motion graphs. Concept Check  Question 1 What are the two ways mentioned in the video to measure how things move? a) Drawing on a graph and using equations b) Drawing on a graph and using pictures c) Using equations and using pictures d) Using equations and using words  Question 2 What information can graphs provide about movement? a) Displacement, velocity, acceleration, and time b) Displacement, position, speed, and time c) Distance, speed, acceleration, and time d) Distance, position, acceleration, and time  Question 3 What is the purpose of drawing a tangent line on a position versus time graph? a) To find the instantaneous velocity b) To find the average velocity c) To find the displacement d) To find the acceleration  Question 4 How is the slope of a tangent line calculated? a) Change in time divided by change in position b) Change in velocity divided by change in time c) Change in position divided by change in time d) Change in time divided by change in velocity  Question 5 What does a straight line going up on a position versus time graph represent? a) Positive acceleration b) Negative acceleration c) Positive constant velocity d) Negative constant velocity  Question 6 What does a line going down on a position versus time graph indicate? a) Positive constant velocity b) Negative constant velocity c) Positive acceleration d) Negative acceleration  Question 7 How is displacement calculated on a position versus time graph? a) Initial time minus final time b) Final time minus initial time c) Initial position minus final position d) Final position minus initial position  Question 8 What does a horizontal line on a velocity versus time graph represent? a) Constant velocity b) Changing velocity c) Positive acceleration d) Negative acceleration  Question 9 How is instantaneous acceleration calculated on a velocity versus time graph? a) Find the slope of a tangent line b) Find the slope of a horizontal line c) Find the area under the curve d) Find the area above the curve  Question 10 Which type of graph shows acceleration versus time? a) Position versus time graph b) Velocity versus time graph c) Displacement versus time graph d) Acceleration versus time graph Motion Graphs Recall  Recall s s Recall velocity Constructing Graphs Graphical Examples Position / Distance / Displacement versus Time graph Consider an object moving at this rate shown in the table below: Time (s) 0 1 2 3 4 Displacement (m) 0 2 4 6 8 displacement time Consider an object moving at this rate shown in the table below: Time (s) 0 1 2 3 4 Displacement (m) 0 2 4 6 8 displacement time  Displacement-versus-Time Graph 𝑟𝑖𝑠𝑒 ∆𝑦 𝑦2 − 𝑦1 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑚= = = = 𝑟𝑢𝑛 ∆𝑥 𝑥2 − 𝑥1 𝑡𝑖𝑚𝑒 𝒅 y 𝒗= 𝒕 displacement or position The slope in displacement-vs-time graph is the velocity of the moving time x object. Consider the displacement-vs-time graphs for the following situations: 1.A still object located 2 m from the origin 2.An object moving at a constant velocity 3.An object that starts from 10 m and moves back to the original position 4.An object accelerating away from the origin Displacement-versus-Time Graph 1. A still object located 2 m from the origin Same position as time passes. displacement No change in position = zero displacement. Velocity is zero. time Displacement-versus-Time Graph 2. An object moving at a constant velocity There is a constant change in position as time displacement passes. Velocity is constant. time Displacement-versus-Time Graph 3. An object that starts from 10 m and moves back to the original position There is a constant change in position as time passes. displacement Velocity is constant. time Displacement-versus-Time Graph 4. An object accelerating away from the origin displacement Velocity is increasing. time  Velocity versus Time graph Velocity-versus-Time Graph Consider an object moving at this rate shown in the table below: Time (s) 0 1 2 3 4 Velocity (m/s) 0 2 4 6 8 velocity time Consider an object moving at this rate shown in the table below: Time (s) 0 1 2 3 4 Velocity (m/s) 0 2 4 6 8 velocity time  Velocity-versus-Time Graph 𝑟𝑖𝑠𝑒 ∆𝑦 𝑦2 − 𝑦1 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑚= = = = 𝑟𝑢𝑛 ∆𝑥 𝑥2 − 𝑥1 𝑡𝑖𝑚𝑒 ∆𝒗 y 𝒂= ∆𝒕 velocity The slope in velocity-vs-time graph is the acceleration of the moving object. time x Consider the displacement-vs-time graphs for the following situations: 1.A still object 2.An object moving at a constant velocity of 2 m/s 3.An object accelerating at a constant rate Velocity-versus-Time Graph 1. A still object Same position as time passes. No change in position = no movement Velocity is zero. velocity Acceleration is zero. time Velocity-versus-Time Graph 2. An object moving at a constant velocity of 2 m/s Same velocity as time passes. Velocity is constant. velocity Acceleration is zero. time Velocity-versus-Time Graph 3. An object accelerating at a constant rate Velocity is constantly changing velocity Acceleration is constant. time  KEY CONCEPTS The motion of objects can be graphically illustrated through displacement-vs-time; velocity-vs-time; and acceleration-vs-time graphs.  Summary Displacement-vs- Acceleration-vs- Situation Velocity-vs-Time Time Time A still object located at the origin An object moving at a constant positive velocity An object moving at a constant acceleration  REFERENCES Books Torio, V.A. (2018) Conceptual Science and Beyond General Physics 1. Quezon City. Brilliant Creations Publishing, Inc.