Kinematics in One Dimension

1. Kinematics in One Dimension AP Physics B Chapter 2 Notes

2. Mechanics • Kinematics • Description of how objects move • Translational • Rotational • Dynamics • Force and why objects move • Newton

3. Frames of Reference • Describe motion with words/pictures, equations and graphs • All need a frame of reference • The man is walking 2 m/s eastward on a train moving 20 m/s eastward. Reference Point B Reference Point A Reference Point C

4. Frame of Reference • We typically use a Cartesian reference frame • Standard x and y axes • Three dimensions • Position requires a FOR

5. Distance and Displacement • Distance (d) is total length of path an object travels • Always positive • Displacement (Δx) is change in position of an object • Needs direction (+/-)! • Vector y Distance = 10 x Displacement = 4

6. Speed and Velocity • Average speed is total distance divided by time • Always positive • Average velocity is displacement divided by time • Direction needed (+/-)! • Vector 400 m in 60 seconds

7. Pause for Nomenclature • Any unit change is x2 - x 1 • Averages are denoted with v bars on top • Average velocity is given by: v = • Tells you about change in position over time

8. Concept Check • Demonstrate the motion of an object that has an average speed and an average velocity that are both zero. • Demonstrate the motion of an object that has an average speed and an average velocity that are both nonzero. • Demonstrate the motion of an object that has an average speed that is nonzero and an average velocity that is zero. • Demonstrate the motion of an object that has an average velocity that is nonzero and an average speed that is zero.

9. Sample Problems • P 12 p. 39: A car traveling 88 km/h is 110 m behind a truck traveling 75 km/h. How long does it take the car to reach the truck?

10. Sample Problems • P. 13 pg 39 An airplane travels 3100 km at a speed of 790 km/h, then encounters a tailwind that boosts its speed to 990 km/h for the next 2899km. What was the total time for the trip? What was the average speed of the plane for the trip?

11. Sample Problems

12. Instantaneous Velocity • Instantaneous velocity is the velocity at any given point in time • Or, the average velocity during an infinitesimally short time interval • v =

13. Instantaneous Velocity • Life can be a little more complicated Position Time

14. Acceleration • Acceleration is defined as how fast an object’s velocity is changing (average is a) • Units m/s2 (m/s/s) • Vector quantity!

15. Acceleration • For constant a, we can use: a = a = • For instantaneous a we use the limit: a = • Careful with negative acceleration and deceleration

16. Acceleration Examples • P 19 pg. 40: A sports car moving at constant speed travels 110 m in 5 s. If it then brakes and comes to a stop in 4 s, what is its acceleration in m/s2? • P 26 pg. 40: In coming to a stop , a car leaves skid marks 92 m long on the highway. Assuming a deceleration of 7 m/s2, estimate the speed of the car just before braking.

17. Concept Check • Demonstrate the motion of an object that has zero initial velocity and positive acceleration. • Demonstrate the motion of an object that has zero initial velocity and negative acceleration. • Demonstrate the motion of an object that has positive initial velocity and negative acceleration. • Demonstrate the motion of an object that has negative initial velocity and positive acceleration.

18. Kinematic Equation Variables

19. The Kinematic Equations There are 3 major kinematic equations than can be used to describe the motion in DETAIL. All are used when the acceleration is CONSTANT. We also have equations for average velocity shown earlier (p. 27 in text).

20. Kinematic Equations Example One • P 68, pg. 43: An AP physics student facing his first test tries to hop on a freight train traveling at a constant speed of 6 m/s. Just as an empty box car passes him, the student starts from rest and accelerates at 4 m/s2 to his maximum speed of 8 m/s (he is an AP physics student). How long does it take him to reach the empty box car? What is the distance traveled to reach the box car?

21. Kinematic Equations Example Two • P. 28, pg. 40: Determine the stopping distances for a car with an initial speed of 95 km/h and reaction time of 1 s, for an acceleration of a) -4 m/s2 and b) -8 m/s2

22. Acceleration Due to Gravity • Known as “free fall” • a = g = -9.8 m/s2 • Assume absence of air/drag in most cases, so can assume constant a • Use same equations, apply to y direction

23. Free Fall Examples • P 39 pg. 40: A helicopter is ascending vertically with a speed of 5.2 m/s. At a height of 125 m a package is dropped. How much time does it take to reach the ground? • P 40 pg.40: For an object falling freely from rest, show that the distance traveled during each successive second increases in the ratio of successive odd integers. Note: In reality objects on earth do not accelerate forever, and air resistance leads to terminal velocity.

24. Concept Check • If the velocity of an object is zero, does it mean that the acceleration is also zero? • If the acceleration of an object is zero, does it mean that the velocity is also zero? • Activity: How can you determine your reaction time without a stop watch? Will it be different on the moon?

25. More Complex Example Up and down motion…g is constant but v is not P 46 pg. 41: You point the nozzle of a garden hose vertically upward at a height of 1.5 m above the ground. When you quickly move the nozzle away from the vertical, you hear water striking the ground next to you for another 2 s. What is the water speed as it leaves the nozzle?

26. Common Problems Students Have • I don’t know which equation to use! • Write down known quantities and what you want to know. • Go shopping for an equation that works!

27. Graphical Interpretation of Motion • The slope of a position time graph equals velocity—here a constant 11 m/s • Since v is constant you get a straight line position-time graph

28. Graphical Interpretation of Motion Not all motion is constant velocity, so position-time graphs may be non-linear Interactive Motion Graphs

29. Graphical Interpretation of Motion • Displacement is the area under a velocity-time curve • The area is found accurately with calculus or approximated by using small Δt

30. Sample Problem • Example 2-16 pg. 37: A space probe accelerates uniformly, from 50 m/s at t = 0 s to150 m/s at t = 10 s. How far did it move between t = 2.0 s and t = 6.0 s? Calculate displacement using a "v vs. t" graph.

31. Sample Problem • P 56 pg. 42: Consider time interval A to B at right. (a) Is the object moving in the positive or negative direction? (b) Speeding up or slowing down? (c) Acceleration positive or negative? Now consider D to E and C to D and answer the same three questions.