1 / 43

Chapter 2

Chapter 2. Motion in One Dimension (Kinematics). 2.1 Displacement and Velocity. Distance is a measure of the total motion of an object (how far it has traveled)

ann
Download Presentation

Chapter 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 2 Motion in One Dimension (Kinematics)

  2. 2.1 Displacement and Velocity • Distanceis a measure of the total motion of an object (how far it has traveled) • Displacementis the net distance and direction an object has traveled (straight line distance and direction from starting to ending point) • What’s your distance when you run two laps around a 400 m track? • What is your displacement? • How are they different?

  3. What is the gecko’s displacement? • ∆x = xf - xi • ∆x = 85 cm – 25 cm • ∆x = 60 cm

  4. Displacement continued • Displacement is not always equal to the distance traveled (if you move back and forth) • Displacement can be positiveor negative.

  5. Speed • We use the variable speedto describe how quickly something moves. • Saying a race car, runner, or plane is “fast” is not enough to accurately describe its speed scientifically.

  6. Speed Distance traveled (m) v = d t Speed (m/sec) Time taken (sec)

  7. A bird flies 50 meters in 7.5 seconds. Calculate the speed of the bird in m/sec. Calculate speed

  8. Calculate distance • How far do you go if you drive for 2 hours at a speed of 100 kilometers per hour?

  9. A space shuttle is traveling at a speed of 7,700 m/sec. How far does the shuttle travel in kilometers in one hour? At an altitude of 300 kilometers, the circumference of the shuttle’s orbit is 42 million meters. How long does it take the shuttle to go around the Earth one time? Calculate time and distance

  10. Calculating Speed • Why the letter v is used for speed... • We use the letter v to represent speed in a formula. • We already used the letter s for seconds • Speed is a single measurement that tells how fast you are going, like 100 km/h. • Velocity means you know both your speed and your direction.

  11. Instantaneous Speed and Velocity • Instantaneous speed is distance ÷ time interval • when the time interval is made very small

  12. Average Speed • Average Speed is the TOTAL DISTANCE divided by the TOTAL TIME • When is Average Speed = Instantaneous speed?

  13. Velocity • Average velocity is displacementdivided by the time interval

  14. 2.2 Acceleration • Acceleration measures the rate of change of velocity • When an object speeds up or slows down it is accelerating. • When an object is speeding up its acceleration is positiveand when it is slowing down its acceleration is negative • Acceleration movie

  15. Constant Acceleration • Constant acceleration is sometimes called uniform acceleration. • A ball rolling down a straight ramp has constant acceleration. constant acceleration increasing speed

  16. Acceleration and Speed • An object can have acceleration, but no speed. • Consider a ball rolling up a ramp. • As the ball slows down, eventually its speed becomes zero. constant negative acceleration decreasing speed

  17. Speed vs Velocity • We frequently use the terms speed and velocity interchangeably • But remember that velocity is speed in a particular direction • So speed is always a positivenumber • Whereas velocity can be a negativenumber if you are going backwards.

  18. Slope and Acceleration • Use slopeto recognize when there is acceleration in speed vs. time graphs. • Level sections (A) on the graph show an acceleration of zero. • The highest acceleration (B) is the steepest slope on the graph. • Sections that slope down (C) show negative acceleration (slowing down).

  19. The slopeof a graph is equal to the ratio of rise to run. The riseis the amount the speed changes. The runis the amount the time changes. Slope of a graph

  20. Accelerationis the change in speed over the change in time. The slope of a speed vs time graph is acceleration. Acceleration and slope

  21. Calculating Acceleration • The formula for acceleration can be expressed several ways But we often write it as:

  22. Acceleration units • Acceleration is a unit of distance divided by a unit of time squared. • In physics we generally use the unit: m/s2 (meters per second per second)

  23. A biker goes from a speed of 0.0 m/s to a final speed of 25.0 m/s in 10 seconds. What is the acceleration of the bicycle?

  24. Kinematics Equations • You should now know how to calculate average velocity and average acceleration using the equations for velocity and acceleration. • Next we will combine them so that you can solve any problem related to objects that are moving at a constant velocity or accelerating. • We need 3 more equations to do this.

  25. Finding displacement (∆x) when you know initial and final velocity and time • The first equation allows you to find displacement when you know the initial and final velocity of an object and the time that it accelerated.

  26. Question: A sports car accelerates from rest to a velocity of 25 m/s in 5.0 seconds. How far did it travel?

  27. Finding displacement (∆x) when you know initial velocity, acceleration, and time. • The second equation allows you to find displacement when you know initial velocity, acceleration, and time (but not final velocity). • You used this equation to determine how high your tennis ball went.

  28. Question: A car traveling at 30 m/s brakes for 3.0 seconds at an acceleration of -2.0 m/s2. How far did it travel during this time? • )

  29. Finding final velocity when you know initial velocity, acceleration, and time • The third equation is used to final velocity when you know initial velocity, acceleration, and time

  30. Question: A jet plane accelerates from rest down a runway for 12 seconds at an acceleration of 15 m/s2. What is it’s final velocity?

  31. Using the Equations of Kinematics • Choose a positive direction • Draw a picture • Make a chart of initial conditions • Choose an equation to solve for the unknown • Solve and check answer for reasonability

  32. Kinematics Example #1 A car accelerates from a stop light for 20.0 s with an acceleration of 5.0 mph/s2. Find its velocity at the end of this time. How far has it traveled?

  33. Kinematics Example #1 V = 100 mph X = 0.278 miles 

  34. Kinematics Example #2 A 747 airliner needs to achieve a speed of 360 km/h to take off. If acceleration is uniform and the runway is 1.8 km long, what acceleration is needed?

  35. Kinematics Example #2 10 km/h/s or 2.78 m/s2

  36. Kinematics Example #3 A penny is dropped from a building rooftop and takes 6.0 s to hit the ground. What velocity does it hit the ground with? How tall is the building in meters? in feet? How would this change if you accounted for the speed of sound?

  37. Kinematics Example #3 H=176m = 579ft V=58.8 m/s 

  38. Example #4 A High Speed Chase • In a high speed chase, a police car takes off after a getaway car going at its maximum speed of 90 mph. The police car accelerates at a rate of 10 mph/s to a maximum speed of 120 mph. How long does it take to catch the bad guys?

  39. Free Fall • An object is said to be in “free fall” if it experiences only a force of gravity. • We abbreviate the accel. of gravity as “g” • g=9.81m/s2 near the Earth’s surface

  40. What goes up… • A ball is tossed in the air.. • When is its velocity 0? • When is its acceleration positive? Negative?

  41. Kinematics Example # 4 • A ball is thrown straight up in the air with an initial velocity of 25.0 m/s. How long will it take for the ball to reach its starting point? What will the ball’s velocity be when it returns to its starting point?

  42. Kinematics Example # 6 t = 5.08 s vf = 25.16 m/s 

  43. The End…

More Related