Physics Unit 1

1. Physics Unit 1 One-Dimensional Motion

2. 1-D Motion • Motion in one direction. • Dependant on the specific, chosen frame of reference • A coordinate system for specifying the precise location of objects in space • Described by displacement, velocity, and acceleration.

3. Displacement • The change in position of an object ∆x = xf – xi displacement=final position – initial position ∆ (delta) means change or change in

4. . . . Good News . . . • Check out figure 2-2 on page 41. • What is the gecko’s displacement? • What would be the gecko’s displacement if we changed the frame of reference so that 0 corresponded to the gecko’s initial position?

5. Displacement What was the car’s displacement? Distance How far did the car travel? Displacement vs. Distance Demo Can they ever be negative? Displacement needs a magnitude (20 cm) and a direction (to the left).

6. Average Velocity • The total displacement divided by the time interval during which the displacement occurred vavg=∆x=xf-xi ∆t tf-ti average velocity=change in position=displacement change in time time interval Velocity, the rate of change of position, can be positive or negative depending on the displacement.

7. Velocity Example Mr. Burr travels from Greencastle to Middletown (50 km). If the first half of the distance is driven at 100 km/h and the second half is driven at 50 km/h, what is the average speed?

8. Sample Problem • During a race on level ground Colin runs with an average velocity of 8.04 m/s to the east. What distance does Colin cover in 243 s?

9. Practice 2A • Try: 2,4,6 on pg 44 • Answers follow: • 3.1 km to the south, 3.00 h, 6.4 h and 77km/h to the south.

10. Distance vs. Time Graphs A BCDE Distance (m) Time (s)

11. Graph 1 Graph 2 Graph the distance/time graphs on graph paper.

12. Graphing Continued • What is the shape of each graph? • Calculate the slope of the black data. • Calculate the velocity of the corresponding object. How do they compare? • What about the slope of the orange data? • Calculate the velocity for each data point.

13. Graphing Continued On a separate sheet of graph paper plot a velocity/time graph for both data sets. • What is the shape of each graph? • What is the slope of each graph? • The slope is the acceleration of the objects.

14. D v T V v T A v T

15. Acceleration • Just like displacement over time gave velocity (rate of change of position), velocity over time will give acceleration (rate of change of velocity). aavg=∆v=vf-vi ∆t tf-ti average acceleration = change in velocity change in time Acceleration must have a direction as well, so it can be positive or negative.

16. Sample Problem The last time Mr. Burr rode his motorcycle he was thrown off and skidded on the blacktop for about 4 seconds. Before the accident he was traveling at 40 km/h. What acceleration was I (he) subjected to?

17. Practice 2B • Do 2 and 4 on page 49 • Answers follow • 2.0 s and -3.5 x 10-3 m/s2

18. Homework • Practice 2A pg 44: • 1,3,5 • Section Review pg 47: • 2,3,5 • Practice 2B pg 49: • 1,3,5

19. Will the car speed up, slow down, retain a constant velocity or not move?

20. Motion with Constant Acceleration • Some systems will have a variable acceleration while some will have constant acceleration. • Free Fall (gravity) • Kinematic Equations • Equations defining displacement and velocity in terms of position, time, velocity and constant acceleration.

21. Displacement with Constant Acceleration • Start with average velocity: • True with constant acceleration • Solve for ∆x=

22. Sample Problem Mrs. Burr was traveling at a velocity of 30 m/s. As she rounded a turn she noticed a poor, defenseless turkey in the road. She, fearing damage to her car despite the lure of free meat, applied her brakes and slowed to a stop in 3.6 s. How far did she travel while applying her brakes?

23. Sample Problem Continued Givens: Unknowns:

24. Practice 2C • Pg 53: • 2, 4 • Answers follow • 18.8 m and 9.1 s

25. Velocity with Constant Acceleration • From the equation for acceleration: • Solving for vf =

26. Another Displacement Equation • Substitute the equation vf = into our original equation for displacement: ∆x =

27. Sample Problem Courtney fires an arrow from her bow. The arrow undergoes a uniform acceleration of 1.9 x 104 m/s2 in 5.4 ms. What is the final speed of the arrow? Over what distance was the arrow accelerated?

28. Sample Continued Givens: Unknowns:

29. Practice 2D • Pg 55: • 2,4 • Answers follow • 19 m/s; 6.0 x 101 m and 2.5 s; 32 m

30. 2nd Velocity Equation • Velocity in terms of displacement instead of time. vf2=vi2+2a∆x I’ll gladly show the derivation of this at another time to anyone who is interested.

31. Sample Problem After two days worth of notes and equations, Mr. Burr’s class revolts and chases him. In order to escape, Mr. Burr accelerates from rest at a rate of 0.500 m/s2. What would his velocity be after traveling 8.58 m?

32. Sample Continued • Givens: • Unknowns:

33. Practice 2E • Pg 58: • 2,4,6 • Answers follow +21 m/s, +16 m/s, +13 m/s; 87 m; 7.4 m

34. Form to use with some initial velocity ∆x=½(vi+vf)∆t vf=vi+a(∆t) ∆x=vi(∆t)+½a(∆t)2 vf2=vi2+2a∆x Form to use when starting from rest ∆x=½(vf)∆t vf=a(∆t) ∆x=½a(∆t)2 vf2=2a∆x Table 2-4: Need to Know and Use

35. Which Equations Do I Use, and When? • Overwhelmed? • Strategy for solving physics problems: • What am I given? (Givens) • What am I looking for? (Unknowns) • Is acceleration constant? (limits the equations one can use) • Which equation(s) give me what I am looking for by using what I already have? (puzzle!) • Plug and Chug!!

36. Strategy Practice • Nathan accelerates his skateboard uniformly along a straight path from rest to 12.5 m/s in 2.5 s. • What is Nathan’s acceleration? • What is Nathan’s displacement during this time interval? • What is Nathan’s average velocity during this time interval?

37. What are You Given? • vi = 0 m/s • vf = 12.5 m/s • ∆t = tf-ti = 2.5 m/s What are You Looking For? • a = ? • ∆x = ? • vavg = ? Acceleration is Constant!!

38. Part 1: a=? • Equations? • aavg=∆v=vf-vi=a (uniform acceleration) ∆t tf-ti • vf=a(∆t) • Pick one and solve.

39. Part 2: ∆x = ? • Equations? • ∆x=½(vf)∆t • ∆x=½a(∆t)2 • vf2=2a∆x • Pick and solve.

40. Part 3: vavg = ? • Equations: • vavg=∆x=xf-xi ∆t tf-ti • Only one equation, so PLUG AND CHUG!!

41. Section Review • Pg 59 • 1,5,6

42. Free Fall • Objects in free fall accelerate at a constant rate, the acceleration due to gravity. • g = 9.81 m/s2 • acts in only the y-axis • same equations apply, change x to y

43. Quick Lab • Pg 62 in book • need meterstick and stopwatch

44. Sample Problem A baseball is hit straight up in the air with a velocity of 25 m/s. Create a table showing the ball’s position (displacement), velocity, and acceleration for the first 5.00 s of its flight. • Givens: • vi = 25.0 m/s • t = 1.00s  5.00 s • g = -9.81 m/s2 • Unknowns: • ∆y and vf for each interval

45. t y v a(s) (m) (m/s) (m/s2) 1.00 20.1 15.2 -9.81 2.00 30.4 5.4 -9.81 3.00 30.9 -4.4 -9.81 4.00 21.6 -14.2 -9.81 5.00 2.50 -24.0 -9.81

46. Homework • Practice 2C • 1,3,5 • Practice 2D • 1,3 • Practice 2E • 1,3,5 • Practice 2F • 1,3,5