Unit 1 Motion Speed, Velocity, and Acceleration PDF

Motion Part 1: Motion and Speed  Position Position is a place where someone or something is located or has been put. In physics, position is usually a number on an axis. You can have an y-axis that is positive value, or could be the y-axis below if the position is negative. Pos...

Motion Part 1: Motion and Speed  Position Position is a place where someone or something is located or has been put. In physics, position is usually a number on an axis. You can have an y-axis that is positive value, or could be the y-axis below if the position is negative. Position means then, a distance from the origin, typically. Speed Speed is the distance an object travels per unit of time. To calculate speed: Speed = Distance ÷ Time Distance is in meters (m) Time is in seconds (s) Speed is in meters per second (m/s) Example 1 A snail takes 5.0 s to crawl across the ruler. Speed Speed Speed ==Distance 0.07 = 2.0m m/s ÷÷5.0 Time s Example 2 A car drives 250 m in one minute. How would you calculate? Speed Speed Speed ==Distance =250 4.17 m ÷m/s ÷60 Time s Use the Formula Triangle! d s t To calculate To calculate To calculate speed: time: distance: s=d/t t=d/s d=sxt  Practice Problem 2 A ball rolled at a speed of 3 m/s for 2.5 s; how far did it travel? d=sxt  Practice Problem 3 How much time will it take you to travel a distance of 150 m at a speed of 30 m/s? Distance vs. Displacement Distance and displacement are different. Distance Displacement How far an object The distance and moves in total. direction an object moves from a starting position. Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position. Distance vs. Displacement Jeffrey, my distance was 176 meters! BE But Billy, your G displacement IN was 1 meter! D EN Distance vs. Displacement 90 ft. Distance = 90 ft. Displacement = 90 ft. Distance vs. Displacement 90 ft. 90 ft. Distance = 180 ft. Displacement =127 ft. Distance vs. Displacement 90 ft. 90 ft. 90 ft. Distance = 270 ft. Displacement = 90 ft. Distance vs. Displacement 90 ft. 90 ft. 90 ft. 90 ft. Distance = 360 ft. Displacement = 0 ft. Motion Part 2: Distance-Time Graphs Graphing Speed The motion of an object can be graphed. A distance-time graph shows the motion of a certain object in line graph form. Time is plotted on the horizontal (X) axis Distance is plotted on the vertical (Y) axis Distance-Time Graphs Time (s) Distance (m) The slope of a 0 0 distance-time 1 2 graph is the 2 4 speed 3 6 4 8 5 8 6 8 7 8 8 8 9 12 10 16 Distance-Time Graphs S=D÷T =0÷4 = 0 m/s S=D÷T =8÷4 S=D÷T = 2 m/s =8÷2 = 4 m/s Distance-Time Graphs Constant Constant No speed speed speed (moving away) (moving closer) (standing still) (and faster!) Interpreting a D-T Graph (1) Analysis: The distance (m) stays the same Distance (m) as the time (s) increases Therefore, the object is at rest Time (s) (not moving) Interpreting a D-T Graph (2) Analysis: The object is moving away Distance (m) from the reference point The object is moving at a constant speed Time (s) The object is moving quickly Interpreting a D-T Graph (3) Analysis: The object is moving towards Distance (m) the reference point The object is moving at a constant speed Time (s) The object is moving slowly Interpreting a D-T Graph (4) Analysis: In Part A, the object is moving Distance (m) away at a constant speed B In Part B, the A C object is at rest In Part C, it is Time (s) moving towards at constant speed Displacement-Time Graphs What does it mean when the line goes through the x-axis? pos. (m) pos. (m) time (s) time (s) Constant speed in positive Constant speed in negative direction. direction. Displacement-Time Graphs Curved segments on the D-T graph mean the object’s speed is changing. pos. (m) pos. (m) time (s) time (s) Speeding up in positive Speeding up in negative direction. direction. Displacement-Time Graphs Curved segments on the D-T graph mean the object’s speed is changing. pos. (m) pos. (m) time (s) time (s) Traveling in positive direction, Traveling in negative direction, but slowing down. but slowing down. Displacement-Time Graphs The slope of a Displacement-T graph is equal to the object’s velocity in that segment. change in y 50 slope = change in x position (m) 40 (30 m – 10 m) 30 slope = (30 s – 0 s) 20 10 (20 m) slope = (30 s) 10 20 30 40 time (s) slope = 0.67 m/s Motion Part 3: Velocity and Acceleration Velocity-Time Graphs Review: Speed Speed is the distance an object travels in a specific amount of time. To calculate speed: Speed = Distance ÷ Time Distance is in meters (m) Time is in seconds (s) Speed is in meters per second (m/s) Velocity Sometimes, knowing the speed isn’t enough. For example, sailors must know the speed and direction their boat is travelling in. Velocity is a description of both speed and direction. e.g. a sailboat travelling at 20 kph in a SE direction Velocity Sometimes, knowing the speed isn’t enough. For example, sailors must know the speed and direction their boat is travelling in. Velocity is an example of a vector, a quantity that has both magnitude and direction.  Average Velocity The map below shows the hiker’s route. One way to describe the trip is to find the hiker’s average velocity. If displacement is 4,000 m and it took 50 minutes… What is the average velocity of the hiker?  Instantaneous velocity Saying the hiker’s average velocity is 1.3 m/s does not mean she walked at a rate of 1.3 m/s for every moment of the trip. Instantaneous Velocity describes the velocity of the object at one specific moment in time or at one specific point in its path. Constant Velocity An unchanging velocity; both speed and direction do not change. This graph shows velocity vs. time. Take a notice of the axes. Which line A or B shows a constant velocity for the duration of the trip? Constant Velocity The motion for letter B shows a changing velocity. Segment 1- from 0-20 seconds, there is a slope, what does slope mean? Velocity-Time Graphs If an object isn’t moving, its velocity is zero. N Object is at rest velocity (m/s) time (s) S Velocity-Time Graphs A horizontal line on the V-T graph N means constant velocity. Object is velocity (m/s) time (s) moving at a constant positive velocity. S Velocity-Time Graphs A horizontal line on the V-T graph means constant velocity. N Object is velocity (m/s) time (s) moving at a constant negative velocity. S  Position vs. Time Velocity vs. Time Meaning  Questions: 1. Which time frame shows constant velocity? 2. Are these all positive or negative velocities? Velocity-Time Graphs A velocity-time (V-T) graph shows an object’s velocity as a function of time. A horizontal line = constant velocity. A straight sloped line = constant acceleration. Acceleration = change in velocity over time. Positive slope = positive acceleration. Not necessarily speeding up! Negative slope = negative acceleration. Not necessarily slowing down! Velocity-Time Graphs If the V-T line has a positive slope, the object is undergoing acceleration in positive direction. If v is positive also, object is speeding up. If v is negative, object is slowing down. Velocity-Time Graphs V-T graph has negative slope. N N velocity (m/s) velocity (m/s) time (s) time (s) Negative velocity and S Positive velocity and S negative acceleration: negative acceleration: object is speeding up! (in object is slowing down, negative direction) Velocity-Time Graphs V-T graph has positive slope. N N velocity (m/s) velocity (m/s) time (s) time (s) S Positive velocity and S Negative velocity and positive acceleration: positive acceleration: object is speeding up! object is slowing down. Velocity-Time Graphs If the V-T line has a negative slope, the object is undergoing acceleration in the negative direction. If v is positive, the object is slowing down. If v is negative also, the object is speeding up. Is the object speeding up or slowing down between Displacement on a velocity vs. time graph Displacement on a velocity vs. time graph Brown = 2 x 2= 4m Yellow= ½ (2) (2)= 2 m Red= ½ (-2) (2)= -2 m Displacement on a velocity vs. time graph A velocity vs. time graph can be used to find the object’s displacement. Displacement equals the velocity multiplied by time. The calculation of displacement is the area of the space between the curve and the axes.  Acceleration Objects can speed up, slow down or change direction. Acceleration measures how much an object’s speed changes over a certain time. Acceleration can be: A change in speed A change in direction A change in speed & direction Acceleration Acceleration can be positive, negative or zero. Object speeds up or Positive Acceleration slows down Object slows down or NegativeAcceleration speeds up Zero Acceleration Constant or no speed Acceleration Formula for acceleration: acceleration = change in velocity time a = Vfinal - Vinitial t Velocity: meters per seconds (m/s) Time: seconds (s) Acceleration: meters per second squared (m/s2) Example 1 A motorcycle’s velocity at the top of the hill is 11.0 m/s. 4.0 seconds later it reaches the bottom of the hill with a velocity of 20.0 m/s. What is the acceleration of the motorcycle? a = Vfinal - Vinitial t a = 20.0 m/s - 11.0 m/s 4.0 a = 9.0 m/s 4.0 a = 2.25 m/s2 Example 2 A speed skater just finished a race. After she crossed the finish line, she coasted to a complete stop. If her initial speed was 13.0 m/s and her acceleration was -2.9 m/s2, how long did it take her to stop? a = Vfinal - Vinitial t - 2.9 m/s2 = 0.0 m/s - 13.0 m/s t t (- 2.9) = - 13.0 m/s t = - 13.0 m/s / - 2.9 t = 4.5 s Do Now: NJSLA Practice Do Now: NJSLA Practice Energy-Remember from lesson 1? In physics, energy is the ability to do work, or the ability to exert a force that causes an object to move. Energy flows any time something gets hotter, colder, faster, slower, or changes, such as when an ice cube melts. Motion Part 4: Position vs. Time Graphs into Speed-Time Graphs Interpreting a D-T Graph Analysis: The distance (m) increasing as Distance (m) time (s) passes The distance gets larger and larger with each second This shows (+) Time (s) acceleration Interpreting a V-T Graph Analysis: The speed (m/s) Velocity (m/s) is increasing as time (s) passes The object speed is changing This shows (+) acceleration Time (s) Interpreting a D-T Graph Analysis: The distance (m) decreasing as Distance (m) time (s) passes The distance gets smaller & smaller with each second This shows (-) Time (s) acceleration Interpreting a D-T Graph Analysis: The distance (m) from a reference Distance (m) point is increasing It is increasing at a regular rate This shows (0) Time (s) acceleration Interpreting a V-T Graph Analysis: The speed (m/s) is constant as velocity (m/s) time (s) passes The object’s speed is not changing This shows (0) Time (s) acceleration Interpreting a D-T Graph (3) Analysis: The object is moving towards Distance (m) the reference point The object is moving at a constant speed Time (s) The object is moving slowly  Exit Ticket How does one graph variables from experimentation? Where does the independent variable belong? Where does the independent variable belong?