1. QotD Draw a model of the following situation A cyclist on a world tour bikes due north for 20 km when he sees a Shell gas station and thinks about getting some water for his trip. But he decides that he will wait until the next station comes up. After another 20 km, he realizes that there are no convenient stores for 30 more km, so he decides to bike back to the Shell station to get water and rest. What is the cyclist’s total distance traveled? What is the cyclist’s total displacement?

2. 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.

3. 2-1 Reference Frames and Displacement The displacement is written: Right: Displacement is positive. Left: Displacement is negative.

4. You and your dog go for a walk to the park. On the way, your dog takes many side trips to chase squirrels or examine fire hydrants. When you arrive at the park, do you and your dog have the same displacement? 1) yes 2) no ConcepTest 2.1Walking the Dog

5. You and your dog go for a walk to the park. On the way, your dog takes many side trips to chase squirrels or examine fire hydrants. When you arrive at the park, do you and your dog have the same displacement? 1) yes 2) no Yes, you have the same displacement. Since you and your dog had the same initial position and the same final position, then you have (by definition) the same displacement. ConcepTest 2.1Walking the Dog Follow-up: Have you and your dog traveled the same distance?

6. Graphing What is the displacement from t 1 = 0 s to t 2 = 9 s? What is the distance traveled during this time?

7. 2-2 Average Velocity Speed: how far an object travels in a given time interval Velocity includes directional information: (2-1)

8. If the position of a car is zero, does its speed have to be zero? 1) yes 2) no 3) it depends on the position ConcepTest 2.3Position and Speed

9. If the position of a car is zero, does its speed have to be zero? 1) yes 2) no 3) it depends on the position No, the speed does not depend on position, it depends on the change of position. Since we know that the displacement does not depend on the origin of the coordinate system, an object can easily start at x = –3 and be moving by the time it gets to x = 0. ConcepTest 2.3Position and Speed

10. You drive 4 miles at 30 mi/hr and then another 4 miles at 50 mi/hr. What is your average speed for the whole 8-mile trip? 1) more than 40 mi/hr 2) equal to 40 mi/hr 3) less than 40 mi/hr ConcepTest 2.4 Cruising Along II

11. You drive 4 miles at 30 mi/hr and then another 4 miles at 50 mi/hr. What is your average speed for the whole 8-mile trip? 1) more than 40 mi/hr 2) equal to 40 mi/hr 3) less than 40 mi/hr It is not 40 mi/hr! Remember that the average speed is distance/time. Since it takes longer to cover 4 miles at the slower speed, you are actually moving at 30 mi/hr for a longer period of time! Therefore, your average speed is closer to 30 mi/hr than it is to 50 mi/hr. ConcepTest 2.4 Cruising Along II

12. 2-3 Instantaneous Velocity These graphs show (a) constant velocity and (b) varying velocity.

13. Position (m) Using graphs to determine velocity Time (s) (60m-20m)/(35s-15s)=2m/s negative velocity (90m-50m)/(110s-85s)=0.004m/s

14. ConcepTest 2.7Velocity in One Dimension If the average velocity is non-zero over some time interval, does this mean that the instantaneous velocity is never zero during the same interval? If the average velocity is non-zero over some time interval, does this mean that the instantaneous velocity is never zero during the same interval? 1) yes 2) no 3)it depends

15. ConcepTest 2.7Velocity in One Dimension No!!! For example, your average velocity for a trip home might be 60 mph, but if you stopped for lunch on the way home, there was an interval when your instantaneous velocity was zero, in fact! 1) yes 2) no 3)it depends If the average velocity is non-zero over some time interval, does this mean that the instantaneous velocity is never zero during the same interval? If the average velocity is non-zero over some time interval, does this mean that the instantaneous velocity is never zero during the same interval?

16. Your turn: If you are driving 110 km/hr along a straight road and you look to the side for 2.0 s, how far do you travel during this inattentive period? What is that in miles? (1 km = 0.62 mi)

17. Qotd: How do we graph velocity vs time? Calculate slope for given time intervals Plot velocity vs time

18. Motion Graphs Draw the position vs time (x vs t) and velocity vs time (v vs t) graphs for the following situation: A student walking toward their locker at a constant speed and then suddenly realizing they had left something in their classroom and turning around to walk away from their locker at a faster rate

19. 2-4 Acceleration Acceleration is the rate of change of velocity.

20. 2-4 Acceleration Acceleration is a vector, although in one- dimensional motion we only need the sign. The previous image shows positive acceleration; here is negative acceleration:

21. ConcepTest 2.8aAcceleration I If the velocity of a car is non-zero (v  0), can the acceleration of the car be zero? 1) yes 2)no 3)depends on the velocity

22. ConcepTest 2.8aAcceleration I If the velocity of a car is non-zero (v  0), can the acceleration of the car be zero? constantvelocity zeroacceleration Sure it can! An object moving with constant velocity has a non-zero velocity, but it has zero acceleration since the velocity is not changing. 1) yes 2)no 3)depends on the velocity

23. Your turn: A sports car accelerates from rest to 95 km/hr in 6.2 s. What is its average acceleration in m/s 2 ?

24. QotD What’s the difference between negative acceleration and deceleration?

25. 2-4 Acceleration There is a difference between negative acceleration and deceleration: Negative acceleration is acceleration in the negative direction as defined by the coordinate system. Deceleration occurs when the acceleration is opposite in direction to the velocity.

26. The Big Three

28. Question of the Day How much time does Mr. Deer have to cross the street without getting hit?

29. Question of the Day How much time does Mr. Deer have to cross the street without getting hit? Car velocity in picture: 15 m/s Accelerating at 2 m/s 2 Displacement = 45 m You don’t see the deer

30. 2-7 Falling Objects Near the surface of the Earth, all objects experience approximately the same acceleration due to gravity. This is one of the most common examples of motion with constant acceleration.

31. 2-7 Falling Objects The acceleration due to gravity at the Earth’s surface is approximately 9.80 m/s 2.

32. When throwing a ball straight up, which of the following is true about its velocity v and its acceleration a at the highest point in its path? 1) both v = 0 and a = 0 2) v  0, but a = 0 3) v = 0, but a  0 4) both v  0 and a  0 5) not really sure ConcepTest 2.8bAcceleration II

33. y At the top, clearly v = 0 because the ball has momentarily stopped. But the velocity of the ball is changing, so its acceleration is definitely not zero! Otherwise it would remain at rest!! When throwing a ball straight up, which of the following is true about its velocity v and its acceleration a at the highest point in its path? 1) both v = 0 and a = 0 2) v  0, but a = 0 3) v = 0, but a  0 4) both v  0 and a  0 5) not really sure ConcepTest 2.8bAcceleration II Follow-up: …and the value of a is…?

34. 2-8 Graphical Analysis of Linear Motion The displacement, x, is the area beneath the v vs. t curve.

35. QotD From memory, write out the BIG 3 equations for constant acceleration motion

36. Free Fall Practice: How long does it take King Kong to fall straight down from the top of the Empire State Building (380 m high)? What is his velocity just before landing?

37. Practice Question (WA Help) In coming to a stop, a car leaves skid marks 92 m long on the highway. Assuming a deceleration of 7.00 m/s 2 estimate the speed of the car just before braking. (P 2.26)

38. QotD: An aircraft needs to be going at a speed of 33 m/s to lift off the ground. The acceleration provided by the engines is 3.5 m/s 2. How long does the runway need to be so the plane can take off?

39. Your turn: A world-class sprinter can burst out of the blocks to essentially top speed (of about 11.5 m/s) in the first 15.0 m of the race. What is the average acceleration of this sprinter, and how long does it take her to reach that speed? Model: Knowns: Unknowns: Equations: