How can acceleration be found from a velocity time graph

The acceleration shown in the purple line can be calculated as follows:. This is the gradient of the purple line. We can calculate the acceleration shown in the first section of the green line as follows:. This is the gradient of the first section of the green line. Velocity-time graphs The velocity of an object is its speed in a particular direction. You have to interact with it! And that's exactly what you do when you use one of The Physics Classroom's Interactives.

We would like to suggest that you combine the reading of this page with the use of our Two Stage Rocket Interactive. This Interactive is found in the Physics Interactives section of our website and allows a learner to apply the skill of calculating slopes and relating them to acceleration values for a two-stage rocket. Visit: Two Stage Rocket Interactive. Next Section: Area Under v-t Graphs.

Time Graphs » Slope of v-t Graphs. An object uniformly accelerates from What is the rate of What is its An object travels 8. How long does this require? Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4. Changes were made to the original material, including updates to art, structure, and other content updates.

Skip to Content Go to accessibility page. Physics 2. Time Graphs. My highlights. Table of contents. Chapter Review. Test Prep. By the end of this section, you will be able to do the following: Explain the meaning of slope and area in velocity vs. Teacher Support The learning objectives in this section will help your students master the following standards: 4 Science concepts. The student knows and applies the laws governing motion in a variety of situations.

The student is expected to: A generate and interpret graphs and charts describing different types of motion, including the use of real-time technology such as motion detectors or photogates. Teacher Support Ask students to use their knowledge of position graphs to construct velocity vs. Maze Game In this simulation you will use a vector diagram to manipulate a ball into a certain location without hitting a wall. Click to view content. If a person takes 3 steps and ends up in the exact same place as their starting point, what must be true?

Figure 2. The slope of a d vs. This is shown at two points. Instantaneous velocity at any point is the slope of the tangent at that point. Teacher Support Return to the scenario of the drive to and from school. Using Velocity Graph to Calculate Some Stuff: Jet Car Use this figure to a find the displacement of the jet car over the time shown b calculate the rate of change acceleration of the velocity.

The displacement is given by finding the area under the line in the velocity vs. The acceleration is given by finding the slope of the velocity graph. The instantaneous velocity can just be read off of the graph. Teacher Support The quantities solved for are slightly different in the different kinds of graphs, but students should begin to see that the process of analyzing or breaking down any of these graphs is similar.

Because this graph is an undefined curve, we have to estimate shapes over smaller intervals in order to find the areas. Like when we were working with a curved displacement graph, we will need to take a tangent line at the instant we are interested and use that to calculate the instantaneous acceleration. The instantaneous velocity can still be read off of the graph. We will find the average velocity the same way we did in the previous example.

Teacher Support Finding the tangent line can be a challenging concept for high school students, and they need to understand it theoretically. Describe the graph and explain what it means in terms of velocity and acceleration.

Teacher Support In this lab, students will use the displacement graph they drew in the last snap lab to create a velocity graph.