Motion in One Dimension Chapter 2

1. Motion in One DimensionChapter 2

2. 2.1 Displacement & VelocityLearning Objectives • Describe motion in terms of displacement, time, and velocity • Calculate the displacement of an object traveling at a known velocity for a specific time interval • Construct and interpret graphs of position versus time

3. Scalar Quantities & Vector Quantities • Scalar quantities have magnitude • Example: speed 15 m/s • Vector quantities have magnitude and direction • Example: velocity 15 m/s North

4. Displacement • Net change in position of an object • Straight line distance from beginning to end • Is not the same as distance

5. Displacement • Displacement is a vector quantity • Indicates change in location of a body ∆x = xf - xi • It is specified by a magnitude and a direction. • Displacement does not take into account the path followed between xi and xf .

6. Displacement is change in position www.cnx.org

7. Describing Motion Describing motion requires a frame of reference http://www.sfu.ca/phys/100/lectures/lecture5/lecture5.html

8. Determining Displacement In these examples, position is determined with respect to the origin, displacement wrt x1 http://www.sfu.ca/phys/100/lectures/lecture5/lecture5.html

9. Indicating Direction of Displacement Direction can be indicated by sign, degrees, or geographical directions.

10. Displacement • In this example, the body moved 10 units to get from A to B. • Distance = length traveled = 10 units • Displacement = net change in position ≈ 5.1 units, NE

11. Velocity

12. Velocity • Example • A squirrel runs in a westerly direction from one tree to another, covering 55 meters in 32 seconds. Calculate the squirrel’s average velocity • vavg = ∆x / ∆t • vavg = 55 m / 32 s • vavg = 1.7 m/s west

13. Velocity is not Speed

14. Position-time graphs(x-t graphs)

15. Velocity can be interpreted graphically: Position Time Graphs

16. Velocity can be interpreted graphically: Position Time Graphs

17. Calculate the average velocity for the entire trip

18. Position-Time Graphs Object at rest? Traveling slowly in a positive direction? Traveling in a negative direction? Traveling quickly in a positive direction? dev.physicslab.org

19. Instantaneous Velocity • Is not average velocity • Is velocity of an object at any given moment in time or at a specific point in the object’s path

20. Position-time when velocity is not constant

21. Instantaneous Velocity • Velocity at any point on an x-t graph • Velocity at a given point in time • Is the slope of a line tangent to the x-t curve

22. Average velocity compared to instantaneous velocity Instantaneous velocity is the slope of the tangent line at any particular point in time.

23. 2.2 Acceleration

24. 2.2 AccelerationLearning Objectives • Describe motion in terms of changing velocity • Compare graphical representations of accelerated and non-accelerated motions • Apply kinematic equations to calculate distance, time, or velocity under conditions of constant acceleration

25. X-t graph when velocity is changing

26. Changes in Velocity • Acceleration is the rate of change of velocity • a = ∆v/∆t • a = (vf – vi) / (tf – ti) • Since velocity is a vector quantity, velocity can change in magnitude or direction • Acceleration occurs whenever there is a change in speed or direction of movement.

27. Dimensions of acceleration • a = ∆v/∆t • = meters per second per second • = m/s/s • = m/s2 • Sample problems 2B

28. Acceleration is a vector quantity • Has magnitude and direction • Both velocity & acceleration can have (+) and (-) values • Whether –a indicates slowing down or speeding up depends upon the sign of velocity

29. Velocity-Time Graphs What would a position-time graph look like? Acceleration-time graph? www.gcsescience.com

30. Free-fall motion graphs v-t graph x-t graph

31. www.gcsescience.com

32. dev.physicslab.org

33. Velocity & Acceleration Velocity acceleration_ __ Motion + + speeding up (-) (-) speeding up + (-) slowing down (-) + slowing down

34. Displacement with Constant Acceleration

35. Final velocity of an accelerating object

36. Displacement during constant acceleration

37. Final velocity after any displacement A baby sitter pushes a stroller from rest, accelerating at 0.500 m/s2. Find the velocity after the stroller travels 4.75m. (p. 57) Identify the variables. Solve for the unknown. Substitute and solve. Practice 2E, p. 58

38. Kinematic Equations

39. 2.3 Falling Objects Objectives • Relate the motion of a freely falling body to motion with constant acceleration. • Calculate displacement, velocity, and time at various points in the motion of a freely falling object. • Compare the motions of different objects in free fall.

40. Free Fall • In the absence of air resistance, all objects fall to earth with a constant acceleration • The rate of fall is independent of mass • In a vacuum, heavy objects and light objects fall at the same rate. • The acceleration of a free-falling object is the acceleration of gravity, g • g = 9.81m/s2 memorize this value!

41. Free Fall • Free fall is the motion of a body when only the force due to gravity is acting on the body. • The acceleration on an object in free fall is called the acceleration due to gravity, or free-fall acceleration. • Free-fall acceleration is denoted with the symbols ag(generally) or g(on Earth’s surface).

42. Free Fall Acceleration • Free-fall acceleration is the same for all objects, regardless of mass. • This book will use the value g= 9.81 m/s2. • Free-fall acceleration on Earth’s surface is –9.81 m/s2 at all points in the object’s motion. • Consider a ball thrown up into the air. • Moving upward: velocity is decreasing, acceleration is –9.81 m/s2 • Top of path: velocity is zero, acceleration is –9.81 m/s2 • Moving downward: velocity is increasing, acceleration is –9.81 m/s2

43. Free-Fall Problem • A tennis ball is tossed vertically with an initial velocity 0f 6.0 m/s. How high will the ball go? How long will the ball be in the air until it returns to its starting point? • Known: vi = 6.0 m/s; a = -g = -9.81 m/s2 • How high? vf2 = vi2 + 2aΔy solve for Δy • vf = vi + aΔt solve for Δt • Since the ball goes up Δt and comes down Δt, time in the air is 2Δt

44. Sample Problem • Falling Object • Jason hits a volleyball so that it moves with an initial velocity of 6.0 m/s straight upward. • If the volleyball starts from 2.0 m above the floor, • how long will it be in the air before it strikes the floor?

45. Sample Problem, continued 1. Define Given: Unknown: vi= +6.0 m/s Δt = ? a = –g = –9.81 m/s2 Δy = –2.0 m • Diagram: • Place the origin at the • Starting point of the ball • (yi = 0 at ti = 0).

46. 2. Plan Choose an equation or situation: Both ∆t and vf are unknown. We can determine ∆t if we know vf Solve for vf then substitute & solve for ∆t 3. Calculate Rearrange the equation to isolate the unknowns: vf= - 8.7 m/s Δt = 1.50 s