Here is an activity that will help your students discover this relationship. Give Part 1 to half the class and Part 2 to the other half. Part 3 on the back of Part 1 and Part 2 is the same for both groups. Also see: A Note on Speed for the purely analytic approach. Like Like. On the AP test, can students just draw a graph of speed as the absolute value of velocity and then notice that speed is increasing or decreasing? Twyla Good question. In these questions they want to see the value of the acceleration and velocity at the time given.
If not the value then some indication as to their signs that the student has worked out. If they have the same sign, then the speed is increasing, if they have different signs then decreasing. I also like to discuss with my students, using the graph, the acceleration of the function. You alluded to this in your example. Looking at the graph we would see where the function was below the axis and where the slope of the tangent line was negative.
OR Looking at the graph we would see where the function was above the axis and where the slope of the tangent line was positive. Thanks Paul.
I think I meant to include it with the original post. You are commenting using your WordPress. You are commenting using your Google account. You are commenting using your Twitter account. You are commenting using your Facebook account. Notify me of new comments via email. Notify me of new posts via email. This site uses Akismet to reduce spam. Learn how your comment data is processed.
The short answer is Speed is increasing when the velocity and acceleration have the same sign. Speed is decreasing when the velocity and acceleration have different signs. Thinking of the speed as the non-directed distance from the velocity to the axis makes answering the two questions below easy: What are the values of t at which the speed obtains its local maximum values?
When do the minimum speeds occur? What are they? Answer: the speed is zero at b and d Students often benefit from a verbal explanation of all this. If you step on the gas your, acceleration pulls you in the direction you are moving and your speed increases.
Then you shift into reverse and start moving backwards negative velocity and you push on the gas to accelerate in the negative direction, so your speed increases. Like this: Like Loading Related posts. Hi Lin, I do like your approach with the reflection of the graphs!!! Speed would be increasing when the velocity and acceleration have the same sign… Looking at the graph we would see where the function was below the axis and where the slope of the tangent line was negative.
Connect and share knowledge within a single location that is structured and easy to search. Based on this graph i have to figuere out when the particle is speeding up and when it is slowing down.
My understanding is that when velocity and accelaration have the same sign then we are speeding up. Using this concept i applied it to this problem and i came up speeding up using interval notation. Thanks Miguel. You've got the right idea, but not the right execution. The position displacement is increasing, so the velocity is positive. Just after these points in time it is moving.
That means that it must be slowing down at those points in time. Acceleration is a 2nd derivative, so you have to pay attention to where the graph holds water and spills water. Where it holds water, the acceleration is positive, and where it spills, it is negative.
A particle usually speeds up when the velocity and the acceleration have the same signs. It slows down when the acceleration and velocity signs are different. My advice even though it might take a while would be to sketch the curve from the given function. Then, you can find where the particle speeds up and slows down. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group.
Create a free Team What is Teams? Learn more. Asked 8 years, 8 months ago. Active 2 years ago. Viewed k times. Miguel Miguel 7 7 gold badges 10 10 silver badges 18 18 bronze badges. Add a comment.
Active Oldest Votes. Now check where the signs match. Cameron Buie Cameron Buie
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