Chapter 2: Kinematics

1. Chapter 2: Kinematics • 2.1 Motion in One Dimension • 2.2 Uniform Motion • 2.3 Instantaneous Velocity • 2.4 Finding Position from Velocity • 2.5 Motion with Constant Acceleration • 2.6 Free Fall • 2.7 Motion on an Inclined Plane • 2.8* Instantaneous Acceleration

2. Motion in one dimension • Determining the signs of position, velocity and acceleration

3. Position vs time graphs

4. Interpreting a position graph 1.What is the position at t =0min 2.What is the position at t =30min 3.What is the velocity at t = 20min 4.What is the velocity at t = 40min

5. Uniform Motion • V(avg)= comstant • The position-vs-graph is a straight line • Vs = ∆s/ ∆t • Sf = Si + Vs ∆t

6. Position –vs time • What we can learn in this Figure?(a) what is the velocity during A? (b) what is the velocity during B? (c) what is Velocity during C?

7. Instantaneous velocity • Using motion diagrams and graphs

8. Stop to think 2.2 C

9. quizzes • Graph a vs b; which is horizontal axis? • How to find the slop of a straight-line graph? y/x or Δy/Δx? • Does the slop have units? If yes, how to determine the units? • How to find the slop at a point on a curvilinear graph?

10. Relating a velocity graph to a position graph The value of the velocity at Any time equals the slope of The position graph T

11. Using calculus to find the velocity Ex. A particle’s position is given by the function 1.What is particle’s position at t = 2s? x = -8+6 = -2 m 2. What is the velocity at t = 2s V|t=2 = -3(2)2+3=-9 m/s

12. Finding position from Velocity

13. Example 2.10 Where is particle’s turning point?

14. Motion with constant acceleration Definition of acceleration If set t0=0s, ∆t = t See page 57

15. Example 2.14A rocket sled accelerates at 50m/s2 for 5.0 s. Coasts for 3.0 s, then deploys a parachute and decelerates at 3.0m/s2 until coming to a halt. What is the maximum velocity of the rocket sled? What is the total distance traveled?

16. Free Fall g = 9.8m/s2 If we choose the y-axis to point vertically up

17. Example 2.16 A falling rockA rock is released from rest at the top of 100-m-tall building.How long does the rock take to fall to the ground, what is impact velocity? • Y0=100m Y1=0m • Vy0= 0 m/s t0 = 0 s

18. Motion on an inclined plane

19. Instantaneous Acceleration

20. Homework 2.54 • A 1000Kg weather rocket is launched straight up. The rocket motor provides a constant acceleration for 16s, then the motor stops. The rocket altitude 20 s after launch is 5100m. You can ignore the air resistance a) What was the rocket’s acceleration during the first 16 s. The rocket launched with Vo = 0, after 16 s b) After motor stops, the acceleration is –g as free fall. c) The rocket’s speed as it passes through a cloud 5100m above the ground

21. Answer the following questions:Two stones are release from rest at certain height on after the other • A) Will the difference in their speed increase, decrease or stay the same Suppose, two stones are release from height h, second stone releases after Δt time from first stone. At any time t, the speed of first stone: V1 = 0 + gt, and V2 = 0 + g(t- Δt ) So that V1-V2 = g Δt , since g is constant, (V1-V2) is constant too. B) Will their separation distance increase, decrease or stay the same At any time, the distance from origin of the first stone is S1 = 0 + 1/2gt2 , the S2 = 0 + ½ g( t- Δt)2, S1-S2 =g t Δt –1/2g(Δt)2 , it depends on t, the longer of t, the greater of The difference.