Motion Graphs Position vs. time

Vocabulary Position Where you are relative to the origin (reference point/observer) Distance The total length of how far you move in a give time period Displacement Overall change in position (final position – initial position) Average speed Total distance / total time Average velocity Displacement / time Instantaneous speed (or velocity) The speed or velocity at one moment in time Positive acceleration Increasing your velocity Negative acceleration Decreasing your velocity

Anatomy of a Position vs time graph The x-axis represents time The Y-axis represents the object’s position relative to the origin The origin represents where the observer is standing Any points above the x-axis are on the positive side of the observer (North, East, Right, above) Any points below the x-axis are on the negative side of the observer (South, West, Left, Below) The y-intercept shows the initial position of the object A line on the graph represents the motion for that period of time Any point on the graph represents the position of the object at that moment in time A horizontal line represents the object STANDING STILL A diagonal with a negative slope represents moving at a constant velocity in the negative direction A horizontal line represents the object STANDING STILL A diagonal with a positive slope represents moving at a constant velocity in the positive direction

Anatomy of a Position vs time graph Steep lines (high slope) mean the objects are moving fast Shallow lines (low slope) mean the objects are moving slow Lines that crisscross mean the objects pass each other Position (m) Time (s)

Anatomy of a Position vs time graph A curve with an increasing slope means accelerating (this one is in the negative direction) A curve with an increasing slope means accelerating (this one is in the positive direction) A curve with a decreasing slope means slowing down (this one is in the negative direction) A curve with a decreasing slope means slowing down (this one is in the positive direction) Position (m) Time (s)

Anatomy of a Position vs time graph Position (m) Time (s) 2 8 3

Position (m) Standing still on the right Standing still on the left Starting on the left and accelerating to the right Starting on the right and decelerating to the left Starting on the left moving quickly to the right then slowing down A car moving at a constant positive speed, slowing down to a stop then speeding back up to the same constant speed Time (s) Position (m) Time (s) Position (m) Time (s) Position (m) Time (s) Position (m) Time (s) Position (m)

Time (s) Position (m) Time (s) Position (m) Time (s) Position (m) Time (s) Position (m) Time (s) Position (m) Time (s) Position (m) Starting on the left and moving to the right at constant velocity Starting on the right and moving to the right at constant velocity Standing still on the left for 4 seconds then accelerating to the right Starting on the left an moving at a constant speed to the right for 2 seconds then stopping at the observer Starting on the right and moving to the left at a constant velocity, stopping, then turning back around and returning to the original position at the same constant speed Starting at the origin and accelerating to the left then reaching a constant speed

Based on the Position vs. Time graph below, answer the following questions 1.Where is the object when time starts? 2.Where is the object when time ends? 3.What is the object’s displacement? 4.During which time period(s) is the object at rest? 5.During which time period(s) is the object speeding up? Position (m) Time (s)

Based on the Position vs. Time graph below, answer the following questions 6.During which time period(s) is the object slowing down? 7.During which time period(s) is the object moving at a constant velocity? 8.How fast is the object moving at 6 seconds? 9.What is the object’s overall average speed? Position (m) Time (s)

Based on the Position vs. Time graph below, answer the following questions 1.Where is the object when time starts? 2.Where is the object when time ends? 3.What is the object’s displacement? 4.What distance did the object travel? 5.During which time period(s) is the object at rest? Position (m) Time (s)

Based on the Position vs. Time graph below, answer the following questions 6.During which time period is the object moving to the right? 7.During which time period is the object moving to the left? 8.What is the velocity of the object at -2 seconds -4 seconds -8 seconds 9.When does the object turn around? 10.When is the object moving the fastest? Position (m) Time (s)

Position vs. Time Graphs y-intercept slope above x-axis below x-axis flat line positive slope negative slope steep line shallow line increasing slope decreasing slope graphs crossing Do Now: Copy this in your notes and fill out what each piece of a position vs. time graph tells you about the object and its position or motion. HW: Complete position vs. time worksheet

Based on the Position vs. Time graph below, answer the following questions 1.How far apart do the objects start? 2.When do they cross paths? 3.Which one is moving faster? 4.What is the average speed of the red car? 5.How far apart are they after 10 seconds? 6.Which one traveled farther? 7.Do they ever have the same speed? Position (m) Time (s)

Anatomy of a Velocity vs Time graph The x-axis represents time The Y-axis represents the object’s VELOCITY The origin represents a velocity of zero Any points above the x-axis mean the object is MOVING in the positive direction. (North, East, Right, above) Any points below the x-axis mean the object is MOVING in the negative direction (South, West, Left, Below) The y-intercept shows the initial VELOCITY of the object Any point on the graph represents the VELOCITY of the object at that moment in time A horizontal line ON THE X-AXIS represents the object STANDING STILL A diagonal line moving AWAY from the x-axis means accelerating (speeding up) A horizontal line represents the object moving at a CONSTANT velocity A diagonal moving TOWARDS the x-axis means slowing down. Crossing the a-axis means stopping and turning around and speeding back up in the other direction

Anatomy of a Velocity vs time graph The Y-axis represents the object’s VELOCITY 5m/s 10s

Time (s) Velocity (m/s) Standing still on the right Standing still on the left Starting at rest and accelerating to the right Starting at 20m/s to the right and decelerating moving quickly to the right then slowing down A car moving at a constant positive speed, slowing down to a stop then speeding back up to the same constant speed Time (s) Velocity (m/s) Time (s) Velocity (m/s) Time (s) Velocity (m/s) Time (s) Velocity (m/s) Time (s) Velocity (m/s)

Time (s) Velocity (m/s) Time (s) Velocity (m/s) Time (s) Velocity (m/s) Time (s) Velocity (m/s) Time (s) Velocity (m/s) Time (s) Velocity (m/s) moving to the right at constant velocity Moving to the left at a constant velocity Standing still for 4 seconds then accelerating to the right Moving at a constant speed to the right for 2 seconds then stopping slowly moving to the left at a constant velocity, stopping, then turning around and returning to the original position at the same constant speed accelerating to the left then reaching a constant speed

Based on the Velocity vs. Time graph below, answer the following questions 1.How fast and in what direction is the object moving when time starts? 2.How fast and in what direction is the object moving when time ends? 3.How far does the object travel in the first 2 seconds? 4.What total distance did the object travel in 7seconds? 5.What is the average speed of the object? Velocity (m/s) Time (s)

Based on the Velocity vs. Time graph below, answer the following questions 6.When is the object slowing down? 7.What it the acceleration during a.the first 2 seconds b.2-5 seconds c.5-7 seconds 8.Does the object turn around? Velocity (m/s) Time (s)

Based on the Velocity vs. Time graph below, answer the following questions 1.How fast and in what direction is the object moving when time starts? 2.How fast and in what direction is the object moving when time ends? 3.How far does the object travel in the first 3 seconds? 4.What total distance did the object travel in 10 seconds? 5.What is the total displacement of the object after 10 seconds? Velocity (m/s) Time (s)

Based on the Velocity vs. Time graph below, answer the following questions 6.During what interval is the object moving left? 7.During what interval is the object moving right? 8.When is the object speeding up? 9.When is the object slowing down? 10.When does the object turn around? 11.What is the acceleration of the object between 6 and 10 seconds? Velocity (m/s) Time (s)