1. So Far….we have this mess of data….what to do with it all? Take a step back and try and see if we can come to a consensus on a few things Let’s start with our position-time graphs T (sec) X (m) T (sec) X (m) Just like in Unit 1, an object with a steeper slope is covering a greater distance in the same amount of time. Therefore, we can say it’s going faster! Let’s not forget direction. Both objects in both graphs are going in the positive direction and both happen to start at the origin

2. Just to make sure T (sec) X (m) T (sec) X (m) X f X i X f X i T iT f T iT f The change in position (∆X) is greater during the same time interval for the graph on the right. The means the object on the right is going faster than the object on the left.

3. On to the v-t graphs

4. T (sec) V (m/s) V f V i T i T f The slope represents the rate at which velocity changes with time This rate at which velocity changes with time is called acceleration

5. V-t graphs continued… So now we know that slope (m) reveals the acceleration of the object. What about “y” or “x” or “b”? T f T i V i V f V (m/s) T (sec) Variable “x” in y=mx + b Time is on our horizontal axis so we’ll substitute that in for “x” Variable “y” in y=mx + b Velocity is on our vertical axis so we’ll substitute that in for “y” Y-intercept (b) in y=mx + b In this particular graph, the y-int = 0 but the important part is that it stands for initial velocity, so we’ll substitute “V I ” in for “b” So when we put this all together for any given time interval we arrive at an equation like this….

6. Bring it together

7. One important thing to notice about acceleration V (m/s) T (sec) You all remember how to divide fractions right?!?!?! Meters per second per second? What does that mean? Time (s)Velocity (m/s) 00 110 220 330 Let’s pretend that an object has an acceleration of 10 m/s 2 The object is getting faster & faster with time

8. But what about displacement?

9. Calculating displacement when object is constantly accelerating T i T f V i V f Let’s say we are concerned about the change in position only from T i to T f In Unit 1, it was fairly easy because all we had to do was find the dimensions of a rectangle and do length x width But now we have a weird shape The good news is that we can break down this weird shape into much more familiar shapes that we can calculate the area of

10. Displacement and our final equation T i T f V i V f A B

11. Summary of Unit 2 Mathematical Models All this from a single v-t graph!! Just like the x-t & v-t graphs are models, all of these equations are models as well Models that describe constantly accelerated motion Remember: The only reason we needed any of this stuff is because our models from Unit 1 FAILED when attempting to describe accelerated motion