Chapter 2 Kinematics in One Dimension:

Transcription

1 Chapter 2 Kinematics in One Dimension: Vector / Scaler Quantities Displacement, Velocity, Acceleration Graphing Motion Distance vs Time Graphs Velocity vs Time Graphs Solving Problems Free Falling Objects

2 Chapter 2 Kinematics in One Dimension: Describing Motion: Change in Position

3 Describing Motion: 2 Types of Quantities Vector Magnitude and Direction Example: Force Push away from you Pull Towards you Described with arrows or +/- Scaler Direction Only Examples: Mass Temperature Time

4 Measuring Change in Position Distance Scaler Quantity Total distance (total number of steps) EXAMPLE: Track & Field 4 x around the track =1600m (one mile) Displacement Vector Quantity Measured as Straight Line From Start to Finish Can be Positive or Negative EXAMPLE: Track & Field 4 x around Track = zero displacement

5 Rate of Change in Position SPEED Rate of change in distance Scaler Quantity d v = t m/s (meters /second) VELOCITY Rate of change in displacement Vector Quantity d Ԧv = t m/s (meters /second) Speedometer Speed is Magnitude of Velocity Can be: positive North East Right Up negative south west left down

6 Example: What is the average speed? How long will it take to run 1 mile (1600m)? Mens 100 m world record How far will he travel in 1 hour?

7 Rate of Change of Velocity Acceleration Vector Quantity a = Δv Δt = v 2 v 1 t 2 t 1 Deceleration Scaler Quantity Losing Speed (m/s)/s = m/s 2 Any change in velocity is acceleration Gaining or losing speed Changing Direction

8 Examples: A car accelerates from 0 m/s to 25 m/s in 2.9 seconds. What is the acceleration of the car? A car moving at 15 m/s slows to 5.0 m/s in 3.0 seconds. What is the acceleration of the car? How long will it take to stop?

9 Graphing Motion Displacement Time Graph d 5 m 5 m 5 m 5 m 5 m 10m 10m 10m t 4m 4m 4m 4m

10 Displacement Time Graph Constant Velocity Displacement is Directly related to time Slope = Velocity ( Δy Δx = Δd Δt = v) Y-intercept = starting position (d i ) y = mx + b Write equation to describe motion D(m) 12 8 d = vt + d i T(s)

11 An car starts from home and drives at 15m/s due north. A truck starts 250m north of the driver and drives 20 m/s to the south. Write an equation to describe the motion of the car. Write an equation to describe the motion of the truck. d Sketch a graph of the car and trucks motion. When and where do they pass each other? t

12 2m 4m 6m 8m 10m d 12m 9m 6m 3m 5m 4m 3m 1m t

13 Displacement vs time graph Constant Acceleration Displacement is exponentially related to time. Slope is always changing Parabolic Shape d = At 2 + Bt + C (+) acceleration (-) acceleration

14 Velocity vs Time graph V (m/s) 5m/s 5m/s 5m/s 5m/s 4m/s 8m/s 12m/s 16m/s T(s) 8m/s 6m/s 4m/s 2m/s

15 Velocity Time Graphs Constant Acceleration Velocity is directly related to time. Slope = acceleration = Δy Δx = Δv Δt = a y-intercept = initial velocity = v i y = mx + b Write equation that describes the motion in the graph above v = at + v i

16 A car moving at 20 m/s accelerates at 3.5m/s 2 for 10s. Sketch a velocity time graph that represents the motion of the car Write an equation for the motion of the car. What is the final velocity of the car? When is the velocity 45 m/s? V (m/s) T(s)

17 Finding displacement using Velocity vs Time Graphs A cat moves at constant speed of 4m/s for 10 seconds. How far does it travel? A turkey starts from rest and accelerates to 6.0m/s om 10s. How far does it travel? A duck moving at 4m/s accelerates to 10m/s in 10s.. How far does it travel?

18 Finding displacement using Velocity vs Time Graphs The AREA under a velocity vs. time graph is equal to displacement. d = 1 2 v 1 + v 2 t (Area of Trapezoid)

19 Using Graphs to Solve Problems A biker on a green road bike moving at 2.0m/s accelerates at 5m/s 2 for 5 seconds. Sketch a d/t and v/t graph of the bikers motion. How far does the biker travel?

20 Using Graphs to Solve Problems A purple people eater moving at 3m/s accelerates at 5m/s 2 for a distance of 15. Sketch a d/t and v/t graph of the monsters motion. What is the final velocity of the monster?

21 Using Graphs to Solve Problems Problem Solving Hints Draw picture or graph. List all Terms Determine which equations(s) to use Solve equation Plug in Terms EXAMPLE: A runner moving at 3m/s accelerates at 4 m/s2 for 5 seconds. How far does the runner travel? What is the final speed of the runner?

22 Using Graphs to Solve Problems Problem Solving Hints Draw picture or graph. List all Terms Determine which equations(s) to use Solve equation Plug in Terms EXAMPLE: A kitten moving at 5m/s slides across the floor and comes to rest after 10m What was the acceleration of the kitten? How much time did it take to come to rest?

23 FREE FALLING OBJECTS Acceleration due to gravity Constant for all objects a =g =9.8 m/s 2 downward Can be positive or negative depending on reference frame 32 ft/s 2

24 FREE FALLING OBJECTS EXAMPLE: A baseball is thrown straight up with a speed of 15 m/s. How high will it rise? Vi =? Vf at max height=? a = How long will it be in the air? Time up =? Time down =?

25 FREE FALLING OBJECTS A dude jumps from the top of a cliff 10 m high. How long is he in the air? Is there a change in direction? Vi =? D =? a = What is his final speed? Vi =? D =? a =

26 FREE FALLING OBJECTS A rock thrown upwards with velocity of 15 m/s from the top of a building 20 m high. How long is it in the air? Is there a change in direction? Vi =? D =? a = What is its final speed? Vi =? a = Vf =

27 World highest jump What is the Velocity after 30 seconds? How far do they fall? Felix Baumgartner Red Bull Stratos 2012

28 Chapter Summary Vector vs. Scaler Displacement, Velocity, Acceleration Graphing Motion Displacement Graph Slope Equations Velocity Graphs Slope, Area Equations Problems Solving Draw, list, choose, solve Free Falling Objects Acceleration of Velocity / Acceleration at Max height Graphing