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Distance time graph gizmo answer key

Word: displacement, distance travel, tilt, speed, speed Preliminary Information Questions (Do this before using Gizmo.) Dora runs a lap around the track and finishes where she started. Clark runs a 100-yard run on the straight side of the track. 1. Which runner has come a long way? 2. Which runner had a bigger change in position, start to finish? Gizmo Warming Distance-Time Charts Gizmo shows a dynamic graph of a runner's position over time. Distance-Time and Speed-Time Charts Gizmo contains the same chart and adds two new ones: speed vs time chart and time chart vs. distance folded. The chart shown below (and in Gizmo) shows a runner's position (or distance from the starting line) over time. This is most commonly referred to as a location-time chart. Check that the Number of Points is 2. Open the Show chart and Show animation for Runner 1 and Runner 2. 1. Drag the dots to create the chart shown on the right. Runner 1 must have lines (red) (0, 0) and (4, 40) endpoints. ? Runner 2 must have line (blue) (0, 40) and (4, 20) endpoints. 2. Click the green Start button on the stopwatch. Watch the two runners carefully. Speed is a measure of how fast an object moves, regardless of direction, in two different types of runners' movements. Speed can never be negative. Speed describes both speed and direction and can be positive or negative. 1. In Gizmo, make a position-time chart for Runner 1 with the following features: ? There is at least one major change in speed. ? There is at least one major change of direction. Click the Green Start button and watch the runner run. Adjust your chart if necessary to meet the requirements. To the right of your drawing (PASTE) chart. 2. Where was the runner every second? Depending on your chart, fill in all of this except the last column in the table below. (Leave the speed column blank for now.) Tag any number with units 3. To calculate the speed of each time interval, first calculate the runner's speed in that range (? distance distance). If the direction is left to right, the speed is positive. If the direction is right-to-left, the speed is negative. Fill in the speed column of the table above. Use volumes (y/s). When this runner is running to the left (negative speed), what does the position-time chart look like? 4. The slope is the steepness of a chart. To find the slope of a line, divide the change in the y value (incretion) into an x value (run) change. Like speed, the slope can be positive, zero, or negative. Fill in the slope of each segment of your position-time chart in the table below 5 with the runner's speed in each time interval. Review your speeds and the location-time chart you're doing. How to choose the VELOCITY-TIME GRAPH tab, regarding the speed on the left side of the Gizmo 6.On the slope runner of a position-time chart. Use green probes to compare the speed-time chart Graphics. A.How does the speed-time chart show a runner moving fast? B.How does the speed-time chart show a runner moving from left to right? 7. It is a runner's position-time chart on the right. First, i think the sketch (USE LINE DRAW) will look like on the empty axle on the far right of its speed-time chart. Then check 1.In Gizmo answer, make position-time charts shown below. Click the Green Start button and follow the runners run. Sketch (USE LINE DRAW) speed-time charts think about what the second set of axis looks like. (If you can, use a red line for runner 1 and a blue line for runner 2.) Then select the VELOCITY-TIME GRAPH tab in Gizmo. Drawing (PASTE) is the actual chart on the third set of the following axises. 2.Make the position -time charts you want for Runners 1 and 2. Draw them below. Then do the same thing - sketch what you think of what their speed-time charts look like, and then check. 3. Compare speed-time charts with related location-time charts. A. When does two different location-time charts have a matching speed-time chart? B.What information is missing from the speed-time chart? 1.Create a position-time chart for Runner 1 shown on the right. Then fill in the blanks below to explain what you think the runner will do based on this chart. The runner will run the meter in the first 2 seconds, with a speed. His direction. Then he'll run for yards in the next two seconds. His direction. Click the Green Start button and watch the runner go. Were you right? 2. Two students, Gina and Walter, discuss the runner shown above in the chart. ? Gina said the runner moved more than 40 meters. ? Walter said the runner moved less than 40 meters. A. Who do you think is right? 3. Above the left half of the Gizmo, select the DISTANCE TRAVELED tab. What was the total distance the runner travels after 4 seconds? B. Displacement equals the difference between start and end positions. Right displacement is positive, left displacement is negative. What is the displacement shown in the chart at the top of the page? 4. In Gizmo, create a position-time chart of a runner with these characteristics: ? Travels a distance of 60 meters in 4 seconds ? has an displacement of your +10 meter Sketch (PASTE) chart on the empty axis on the right. 5. See the chart you made in Question 4. Think of the speed of the runner. A. What was the runner's speed for the first 2 seconds? B. What was the runner's speed in the last two seconds? A. What was the runner's average speed in 4 seconds? 6. Now consider the speed of question 4 runner. A. What was the runner's speed for the first 2 seconds? B. What was the runner's speed in the last two seconds? A. What was the runner's average speed in 4 seconds? 7. Let's say you know the time, displacement and total distance for a runner. How do you calculate the runner's average speed? B. How do you calculate the average speed of the runner? 8. A runner on the right is a chart. Calculate the following values for this runner. Add the appropriate units. Student Discovery: Distance-Time Charts Word: speed, y-cut pre-knowledge questions (Do this before using Gizmo.) Max ran 50 meters in 10 seconds. Molly ran 30 meters in five seconds. Who ran farther, Max or Molly? Who runs faster? ____ ________ Explain: Max is running 6 meters per second while Max is running 6 meters per second on a track _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Check that the number of points is 2 and that both the Graphics and Show animation is on under Runner 1. The chart should look as shown on the right ? one point (0, 0) and the other point (4, 40). Click the green Start button on the stopwatch. What's going to happen? Click the red Reset button on the stopwatch. The vertical green end in the chart lets you see a snapshot of the runner at any time. Drag back and back. Like you, watch the runner and the stopwatch. What was the runner's position in a second? _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Activity A: Runner position Prepare Gizmo: Click the red Reset button on the stopwatch. Make sure the number of points is 2. In Gizmo, you run many times in various races of different graphics. (Red dots in the chart can be dragged vertically.) Notice what the chart says to you about the runner. If a distance-time chart contains a point (4, 15), what does that tell you about the runner? (Be precise and answer with a full sentence.) Look at the chart on the right. Watch where the green end is. If you could see the runner and the stopwatch right now, what would you see? Look at the picture below, from Gizmo. What's right about this runner's chart? In a chart, the point lying on the y-axis (vertical axis) is called a y-intercept. What does the Y-intercept tell you about the runner? Set the number of points in Gizmo to 3. Then chart a runner starting at the 20-meter line, running to the 40-meter line and finishing on the 30-meter line. Draw your chart to the right. What is the y-intercept of your chart? _________ Activity B: Prepare runner direction and speed Gizmo: Click the red Reset button on the stopwatch. Run Gizmo several times with different chart types. (Remember, red dots in the chart can be dragged vertically.) Pay attention to the speed and direction of the runner. 1.A forward-running (left (left) Gizmo. Draw your chart to the right. If the runner is moving from left to right in Gizmo, what does the chart always look like? Click the Reset Red button. Chart a right-to-left runner. Draw to the right. What does the chart always look like if the runner is moving from right to left in Gizmo? Change the number of points to 5. Chart a runner that works from left to right for a second, rests for two seconds, and then continues to work in the same direction. Draw the chart to the right. How does a chart show a runner's rest? In general, how does a distance-time chart show which direction the runner is moving in? (Activity B continued on the next page) Activity B (continue from the previous page) Create the chart shown on the right with the number of points set to 3. Your chart must contain (0, 0), (2, 10), and (4, 40). Where does the runner start? Where's he going to be in two seconds? -This will be _________at.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ (Take your answer into the circle below.) Click the Start button and watch the animation. What about the runner who changed after two seconds of running? Speed is a measure of how fast something moves. Divide the distance by time to calculate the speed. In Gizmo, speed units are defined as meters per second (m/s). How far did the runner go in the first two seconds? ? How far did the runner go every second during this time period? - What was the speed of the runner during this time period? - Now look at the last two seconds represented in the chart. How far did the runner go in the last two seconds? How far did the runner go every second during this time period? What was the runner's speed during that time period? Click the Reset button. Experiment with a variety of graphs, focusing on the runner's speed. In general, how can you guess the speed of the runner by looking at a chart? Activity A: Get ready for two runners, two graphics Gizmo: Click Reset. Under Runner 2, open the Show chart and Show Animation. Try experimenting with Gizmo to create each of the following results. (You can use as many dots as you want in your charts.) Each time you find a solution, click the camera (next to the chart). Right-click the picture, and then click Copy Picture. Then paste the picture into a blank document. Tag all five of the. Runner 1 wins the race. Runner 2 wins the race. Runner 2 catches and runner 1 pass. Runner 2 goes in the opposite direction as runner 1. Each runner goes at a different pace, but both reach the finish line together. Based on your experiments, answer the following questions. If a runner starts from the front, how does the chart come about? How does the chart show which runner is faster? How does the chart show which runner won the race? What does it look like when a runner goes back and forth on the chart? What does it mean when two runners' charts intersect? Challenge: Turn off Show for Runner 2 Click New to create a new random chart for Runner 2 that you can't see. Click Start and watch it run. Then try to adjust the graph of runner 1 so that its movements will fit runner 2's movements. To check each response, open the Show chart. (For a bigger challenge, increase the number of points before selecting New.) (Activity C continued on the next page) Activity C (continue from the previous page) Challenge: Use Gizmo to model and solve the following word problems. Type the solutions in the following spaces. Draw the chart you made to resolve the question in the space to the right of each question. A dog chases a cat into a tree. The cat's 10 meters ahead and running at 20 feet per second. The dog runs at 8 meters per second. The tree is 100 feet from the dog's starting position. Which animal will reach the tree first? A police officer is after a bag thief on the street. The thief starts 9 meters in front of the officer and can run 20 meters in 4 seconds (5 m/s). The officer can run 32 meters in 4 seconds (8 m/s). How long before the officer catches the thief? In one football game, one team kicks the other. Right now the receiver catches the ball, he's the closest linebacker 40 yards. The receiver runs from left to right at 10 meters (10 m/s) per second. The defender runs from right to left at 6 meters per second. How long will it take them to collide? How far does the receiver go? A turtle forced a rabbit into a four-hour race. The rabbit is so confident of winning because it allows the turtle to start by a 10km margin. The rabbit runs at 14km/h, but stops for a two-hour nap in the middle of the race. The turtle's been moving at 2 miles an hour the whole race. Who's going farther in four hours? How are distance-time charts useful? Explain and discuss your answer with your teacher and classmates if possible. Class.

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