Review Kinematic Graphs

Names: Nina Feinberg, Eva Bevan, Jordan Bailkin, Emily Truongcao Date: 4/5/21 Student Exploration: Distance-Time and Velocity-Time Graphs Directions: Follow the instructions to go through the simulation. Respond to the questions and prompts in the orange boxes. [NOTE TO TEACHERS AND STUDENTS: This lesson was designed as a follow-up to the Distance-Time Graphs Gizmo. We recommend you complete that activity before this one.] Vocabulary: displacement, distance traveled, slope, speed, velocity Gizmo Warm-up The Distance-Time Graphs Gizmo shows a dynamic graph of the position of a runner over time. The Distance- Time and Velocity-Time Graphs Gizmo includes that same graph and adds two new ones: a velocity vs. time graph and a distance traveled vs. time graph. The graph shown below (and in the Gizmo) shows a runner’s position (or distance from the starting line) over time. This is most commonly called a position-time graph . Check that the Number of Points is 2. Turn on Show graph and Show animation for both Runner 1 and Runner 2 . 1. Drag the points to create the graph shown to the right. ● Runner 1 ’s line (the red one) should have endpoints at (0, 0) and (4, 40). ● Runner 2 ’s line (the blue one) should have endpoints at (0, 40) and (4, 20). 2. Click the green Start button on the stopwatch. Watch the two runners carefully. In what two ways are the runners’ motions different? The red runner (1) runs at a faster speed and well as a farther distance than the blue runner (2) is able to go. C Activity A: Velocity-time graphs Get the Gizmo ready : ● Click the red Reset button on the stopwatch. ● Change the Number of Points to 5. ● Turn off Show graph and Show animation for Runner 2 . Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

Speed is a measure of how fast an object moves, regardless of direction. Speed can never be negative. Velocity describes both speed and direction, and can be positive or negative. 1. In the Gizmo, make a position-time graph for Runner 1 with the following features: ● There is at least one major change in speed. ● There is at least one major change in direction. Click the green Start button and watch the runner run. Adjust your graph if needed to meet the requirements. Hand draw in this space or click here to select ✏ EDIT to use the drawing tool. Sketch your graph to the right. 2. Where was the runner each second? Based on your graph, fill in all except the final column in the table below. (Leave the velocity column blank for now.) Label any numbers with units. Time Position at end of time interval (m) Distance moved this time interval (m) To the left or right? Velocity this time interval (m/s) 0 – 1 sec 7m 7m right 7m/s 1 – 2 sec 12m 5m right 6m/s 2 – 3 sec 34m 22m right 11.3m/s 3 – 4 sec 24m -10m left -6m/s 3. To calculate the velocity for each time interval, first calculate the speed of the runner in that interval (speed = distance ÷ time). If the direction is left to right, velocity is positive. If the direction is right to left, velocity is negative. Fill in the velocity column of the table above. Use units (m/s). When this runner is running to the left (negative velocity), what does his position-time graph look like? The graph looks opposite (going down) compared to the other segments of the graph, where we know the runner is going to the right. 4. Slope is the steepness of a graph. To find the slope of a line, divide the change in y -value (rise) by the change in x -value (run). Like velocity, slope can be positive, zero, or negative. Fill in the slope of each segment of your position-time graph, along with the runner’s velocity during each time interval, in the table below. Time interval Slope Velocity (m/s) Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved

2. Make any position-time graphs you want for Runners 1 and 2 . Hand draw in this space or click here to ✏ select EDIT to use the drawing tool. Sketch them below. Then do the same thing – sketch what you think their velocity- time graphs look like, and then check. 3. Compare the velocity- time graphs to their related position- time graphs. A. When do two different position-time graphs have matching velocity-time graphs? When they have the same velocity or slope A. What information is missing from a velocity-time graph? The runner’s position Reproduction for educational use only. Public sharing or posting prohibited. © 2020 ExploreLearning™ All rights reserved Position-time graph Velocity-time (predicted) Velocity-time (actual) Position-time graph Velocity-time (predicted) Velocity-time (actual)