1. Page 1 Algebraic Analysis of Motion

2. Page 2 Five principal motion variables v o – initial velocity v f – final velocity Δx – displacement a – acceleration t - time

3. Page 3 Steps If it is not given to you already, define a positive direction Make a chart giving the values of the five principal motion variables. Include a sign for each one (except for time) When three out of the five variables are known, the remaining variables can be solved for

4. Page 4 Physics 1 Many times on the AP exam, this will be all you need to do, the question will ask something like, is it possible to determine how much time the engines were running? Actually doing the math is a math skill, not a physics skill. Even if calculations are called for, as long as they are reasonable (a model rocket burns for a few seconds, not thousands of seconds) you will be awarded full credit. However, in class we will both work quantitative and qualitative problems so you know how to do it all!

5. Page 5 The equations Sometimes, you will need to use 2 of these equations so that you don’t have to solve a quadratic equation

6. Page 6 Example #1 Example: A boat moves slowly out of a marina (so as to not leave a wake) with a speed of 1.50 m/s. As soon as it passes the breakwater, leaving the marina, it throttles up and accelerates at 2.40 m/s/s. What do I know? What do I want? v o = +1.50 m/sv f = ? a = +2.40 m/s/s t = 5 s a) How fast is the boat moving after accelerating for 5 seconds? 13.5 m/s Define positive to be moving out of the marina Starting point is breakwater, ending point is 5 seconds later ALWAYS INCLUDE UNITS IN ANSWER!!!!

7. Page 7 Example #1 cont b) How far did the boat travel during that time? 37.5 m

8. Page 8 Does all this make sense? 1.5 m/s 13.5 m/s Total displacement = 7.50 + 30 = 37.5 m = Total AREA under the line.

9. Page 9 Example #2 What do I know? What do I want? v o = +12 m/sΔx = ? a = -3.5 m/s/s v f = 0 m/s Example: You are driving through town at 12 m/s when suddenly a ball rolls out in front of your car. You apply the brakes and begin decelerating at 3.5 m/s/s. How far do you travel before coming to a complete stop? 20.57 m Positive is direction you are moving Start of motion is when brakes are applied, end of motion is when you stop

10. Page 10 Example 3 Positive direction is direction plane is moving Beginning of motion is when the plane touches down, end of motion is when plane is stopped

11. Page 11 Example 4 Positive direction is direction spacecraft is moving Beginning of motion is when the retrorocket fires, end of motion is 215 km later (215000 m)

12. Page 12 Example 5 - qualitative A bus driver makes an emergency stop by slamming on the brakes and skidding to a stop. How far would the bus have skidded if it had been traveling twice as fast? (in comparison to the 1 st )

13. Page 13 Example 6 – Last one! A model rocket is launched straight upward with an initial speed of 50 m/s. It speeds up with a constant upward acceleration of 2.0 m/s 2 until the engine stops at an altitude of 150 m. How much time does it take for this to happen? Positive direction is up Beginning of motion is launch, end of motion is when engine stops