1. Chapter 2 Describing Motion: Kinematics in One Dimension

2. Units of Chapter 2 Reference Frames and Displacement Average Velocity Instantaneous Velocity Acceleration Motion at Constant Acceleration Solving Problems Falling Objects Graphical Analysis of Linear Motion

3. Problems Solving 1. Read the whole problem and make sure you understand it. Then read it again. 2. Decide on the objects under study 3. Draw a diagram and choose coordinate axes. 4. Go through G-U-E-S-S method 5. Look at the result – is it reasonable? Does it agree with a rough estimate?

4. Problem Solving G ivens U nknowns E quations S ubsitute S olve

5. Problem Solving If you travel for 60 miles at 30 mph and then return to where you started from at 20 mph, what is your average speed for the trip? G ivens: d 1 = 60mi t 1 = 30mph d 2 = 60mi t 2 = 20mph U nknowns: v t E quations: v t = d t /t t d t = d 1 + d 2 t t = t 1 + t 2 t 1 = d 1 /v 1 t 2 = d 2 /v 2 S ubstitute: d t = d 1 + d 2 = 60mi + 60 mi = 120mi t 1 = d 1 /v 1 = 60mi/30mph = 2h t 2 = d 2 /v 2 = 60mi/20mph = 3h t t = t 1 + t 2 = 2h + 3h = 5h S olve: v t = d t /t t = 120mi/5h = 24mph

6. 2-1 Reference Frames and Displacement Any measurement of position, distance, or speed must be made with respect to a reference frame. For example, if you are sitting on a train and someone walks down the aisle, their speed with respect to the train is a few miles per hour, at most. Their speed with respect to the ground is much higher.

7. 2-1 Reference Frames and Displacement A train is traveling at 80 mph and you are walking in the direction it’s traveling at 3 mph. 1. What is your speed relative to the train? 2. What is your speed relative to the ground? 3. If you are traveling at 60 mph and hit a car in a head-on collision where that car is traveling in the opposite direction at 50 mph, what is the effective speed of the crash?

8. 2-1 Reference Frames and Displacement We make a distinction between distance and displacement. Displacement (blue line) is how far the object is from its starting point, regardless of how it got there. Distance traveled (dashed line) is measured along the actual path.

9. 2-1 Reference Frames and Displacement Generally, displacement is written: ∆d = d f – d i If displacement is along the x-axis it is written as: ∆x = x f – x i Moving to the right: Displacement is +20. Moving to the left: Displacement is -20.

10. 2-1 Distance vs. Displacement 1.If you travel 2 mi to the North, then 2 mi to the East, then 2 mi to the South, and then 2 mi to the West, what was your distance traveled? 2.In the above situation what was your displacement?

11. 2-2 Average Velocity Speed: how far an object travels in a given time interval Velocity includes directional information: (2-1)

12. 2-2 Speed vs. Velocity 1.You travel 2 mi to the North, then 2 mi to the East, then 2 mi to the South, and then 2 mi to the West, what was your speed if the trip took you 2 hours? 2.In the above situation what was your velocity? 3.You are traveling in a circle at 30 mph. Is your speed constant? 4.You are traveling in a circle at 30 mph. Is your velocity constant?

13. 2-2 Speed Equation Speed: how far an object travels in a given time interval

14. 2-2 Average Speed What was your average speed if you start at 0 m/s and finish at 10 m/s?

15. 2-3 Instantaneous Speed The instantaneous speed is a speed measured at a certain point in time (think radar gun that police use) while the average speed takes your total distance and divides it by the total time In a sprint, your instantaneous speed at the start of the race is zero, so it’s lower than your average speed for the whole race, because it takes you a little time to get up to your top-speed. To measure an instantaneous speed you need motion detectors because using a stopwatch can only get you an average speed (you use a known distance, a start time and a stop time).

16. 2-4 Acceleration Acceleration is the rate of change of velocity.

17. 2-4 Acceleration

18. Acceleration has a direction or a sign The previous slide shows positive acceleration; here it is negative acceleration because the cars velocity decreases:

19. 2-4 Acceleration “Deceleration” occurs when the acceleration is opposite in direction to the velocity. Instantaneous acceleration is the acceleration at a certain point time while average acceleration is change in velocity divided by the change in time.

20. 2-4 Acceleration You are traveling in a circle at 30 mph. Are you accelerating? You can rearrange the acceleration equation: a = ∆v/∆t ∆v = a∆t ∆t = ∆v/∆t