1 / 40

Catalyst—9/02/2016

Catalyst—9/02/2016. Draw a graph with the following information: “position” on y-axis, “time” on x-axis, with the three data points 0, 0 2, 4 4, 8 What is the slope of the line? Turn in Catalyst . Motion Graphs. Motion & Graphs.

charlesmurphy
Download Presentation

Catalyst—9/02/2016

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Catalyst—9/02/2016 • Draw a graph with the following information: “position” on y-axis, “time” on x-axis, with the three data points • 0, 0 • 2, 4 • 4, 8 • What is the slope of the line? • Turn in Catalyst 

  2. Motion Graphs

  3. Motion & Graphs • Motion graphs are an important tool used to show the relationships between position, speed, and time. • It’s an easy way to see how speed or position changes over time • These types of graphs are called kinematic graphs. • There are two types: • Position vs. Time graphs • Speed vs. Time Graphs

  4. Position Vs. Time • Used to show an object’s position at a given time. • Position: on y-axis • Time: on x-axis

  5. You Try It: Graphing Position Vs. Time • Suppose you are helping a friend who is training for a track meet. • She wants to know if she is running at constant speed. • You mark the track in 50-meter increments and measure her time at each position during a practice run. • Create a position-time graph using her data.

  6. You Try It: Graphing Position Vs. Time • When you’ve plotted all 4 points, you should get a graph that looks like this… • What would her speed be? • Choose any point, & divide distance (position) over time

  7. What would her speed be? 50m/10s = 5 m/s 100m/20s = 5 m/s Notice that this is a straight line - why?? She is moving at a constant speed - neither slowing down nor accelerating You Try It: Graphing Position Vs. Time

  8. You Try It: Graphing Position Vs. Time #2 • Graph the motion of this car. • Graph the points: (0,0), (1, 10), (2, 20), (3, 30), (4, 40), (5, 50). • Your graph should look like this… • What is this car’s velocity? • A constant 10 m/s

  9. What does slope have to do with it? • Slope is the ratio of the rise (y-axis) to the run (x-axis) of a line on a graph. • A bigger slope means a steeper line which means a faster speed.

  10. Steeper Line = Faster Speed

  11. Steeper Line = Faster Speed

  12. Negative Slopes • What does this graph mean??? • And this one? • They show an object that is slowing down - or decelerating. • The first graph is slowly decelerating, while the second graph is quickly decelerating.

  13. Basically… You might want to draw thisgraph in your Motion Math Little book

  14. This is another really good graph to draw in yourmotion math little book

  15. Position Vs. Time - Changing Velocity • Now consider a car that has a changing velocity. • It is not moving at a constant rate, but getting faster by the second. • What would this graph look like? • You try it first…

  16. Does your graph look like this? Be sure you have this one drawn

  17. You Try It: GrAPHING Position Vs. Time #3 • What would the graph look like for a car that traveled 10 m in the 1st second, 15 m by the 2nd second, 25 by the 3rd second, and 40 m by the 4th second?

  18. Predict: What does THIS GRAPH show?

  19. This graph is for a car moving with a constant velocity of +5 m/s for 5 seconds, stopping abruptly, and then remaining at rest for 5 seconds. • The straight line means its position is NOT changing.

  20. Speed Vs. Time • Used to show an object’s speed at a given time. • Speed: on y-axis • Time: on x-axis

  21. Speed Vs. Time - Constant Speed • This graph shows the speed versus time for a ball rolling at constant speed on a level floor. • On a speed vs. time graph, constant speed is shown with a straighthorizontal line. • If you look at the speed on the y-axis, you see that the ball is moving at 1 m/s for the entire 10 seconds.

  22. Speed Vs. Time - Constant Speed • Compare this speed-time graph to the position-time graph for the ball. • Both of the graphs show the exact same motion, even though they look different. • If you calculate the slope of the lower graph, you will find that it is still 1 m/s.

  23. You Try It: Graphing Speed Position Vs. Time • Maria walks at a constant speed of 6 m/s for 5 seconds. • Then, she runs at a constant speed of 10 m/s for 5 seconds. • Create a speed-time graph using her data.

  24. Speed Vs. Time - Changing Speed • As we know, most objects don’t move at a constant speed. • If a speed vs. time graph slopes up, then the speed is increasing. • If it slopes down, then the speed is decreasing. • If the graph is horizontal, then the object is moving at a constant speed.YOU MAY WANT TO DRAW THESE GRAPHS TOO!

  25. Putting it All Together • Which runner won the race? • Albert won the race. He reached 100 meters first. • Which runner stopped for a rest? • Charlie stopped for a rest at 50m. • How long did he stop for? • Charlie stopped for 5 seconds. (13-8)

  26. Putting it All Together 4. How long did Bob take to complete the race? • Bob finished the race in 14 seconds 5. Calculate Albert's average speed. • Speed = distance/time • Speed = 100m/12s = • Albert’s Speed = 8.3 m/s

  27. Interpreting Motion Graphs Copy these as Notes!!! Page 13 in notebook

  28. Position vs. Time Graphs Stationary Constant velocity in the positive direction Constant velocity in the negative direction

  29. Position vs.Time graphs Acceleration (Speeding up) in the positive direction Acceleration (Slowing down) in the positive direction

  30. Position vs.Time graphs Acceleration (Speeding up) in the negative direction Acceleration (Slowing down) in the negative direction

  31. Using slope to predict motion • On a position vs. time graph • If slope is 0, then velocity is 0. • If slope is constant positive, velocity is constant. • If slope is constant negative, velocity is constant in the opposite direction. • If slope is changing, velocity is changing. (i.e. you are accelerating)

  32. Velocity vs. Time Graphs Constant Velocity in the positive direction Increasing velocity in the positive direction Decreasingvelocity in the positive direction

  33. Velocity vs. Time Graphs Constant Velocity in the negative direction Increasing velocity in the negative direction Decreasing velocity in the negative direction

  34. Using slope to predict motion • On a velocity vs. time graph • If slope is 0, then velocity is constant. • If there is a non-zero slope, the velocity is increasing or decreasing (i.e. there is an acceleration!)

  35. What is happening?—Practice V (m/s) 50 t (s) 1 2 3 4 5 6 7 -25

  36. What is happening?—Practice

  37. What is happening?—Practice

  38. What is happening?—Practice d t

  39. Draw it! (on a d-t graph) • Laura walks towards the lunchroom at a constant speed. She then realizes that they are serving tater tots for lunch and begins to accelerate. She gets to the lunch line and comes to a stop.

  40. Draw it! (on a v-t graph) • Laura walks towards the lunchroom at a constant speed. She then realizes that they are serving tater tots for lunch and begins to accelerate. She gets to the lunch line and comes to a stop.

More Related