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Speed and Acceleration

Understand speed, velocity, and acceleration concepts, calculate distance and time, interpret speed graphs, and solve motion problems efficiently.

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Speed and Acceleration

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  1. Speed and Acceleration Measuring motion

  2. What Is Motion? • Motion is when an object changes place or position. To properly describe motion, you need to use the following: • Start and end position? • Movement relative to what? • How far did it go? • In what direction did it go?

  3. Measuring Distance • Meter – international unit for measuring distance. 1 mm = 50 m

  4. Calculating Speed • Speed (S) = distance traveled (d) / the amount of time it took (t). • Speed is the distance an object travels in a certain amount of time. S = d/t

  5. Units for speed • Depends, but will always be a distance unit / a time unit • Ex. Cars: mi./h • Jets: km/h • Snails: cm/s • Falling objects: m/s

  6. Calculating speed S = d/t • If I travel 100 kilometer in one hour then I have a speed of… • 100 km/h • If I travel 1 meter in 1 second then I have a speed of…. • 1 m/s

  7. Ways To Calculate Speed • Constant speed is when you are traveling at the same rate of speed, such as 55 mph constantly on a highway. • Average speed is taking the total distance traveled, and dividing by the total time it takes. Used for calculations that involve changing speed. • Instantaneous speed is the speed at any one given point in time.

  8. Average speed • Speed is usually NOT CONSTANT • Ex. Cars stop and go regularly • Runners go slower uphill than downhill • Average speed = total distance traveled/total time it took.

  9. Average Speed • What is the AVERAGE speed of the bass boat depicted in the graph?

  10. Calculating Average Speed • It took me 1 hour to go 40 km on the highway. Then it took me 2 more hours to go 20 km using the streets. • Total Distance: • 40 km + 20 km = 60 km • Total Time: • 1 h + 2 h = 3 hr • Ave. Speed: • total d/total t = 60 km/3 h = 20 km/h

  11. Question • I travelled 25 km in 10 minutes. How many meters have I travelled? • A) 25000 m • B) .0112 m • C) .025 m • D) 2.5 m 25 km * 1000m/km = 25000 m

  12. Question • I ran 1000 m in 3 minutes. Then ran another 1000 m uphill in 7 minutes. What is my average speed? • A) 100 m/min • B) 2000 m/min • C) 10 m/min • D) 200 m/min • E) 20 m/min Total Dist. = 1000 m + 1000 m = 2000 m Total Time = 3 min + 7 min = 10 min Ave speed = total dist/total time = 2000m/10 min = 200 m/min = D

  13. Speed Graphs • In what time period is the bass boat speeding up? • In what time period is the bass boat slowing down? • When is the speed NOT changing?

  14. Instantaneous Speed • What is the instantaneous speed of the bass boat at t=7 seconds?

  15. Instantaneous speed is speed at any given point in time. At 7 seconds, the distance is 85 meters; therefore the IS is

  16. Graphing Speed • Speed is usually graphed using a line graph, and it depicts the distance and time. • Time is the independent variable, and thus is ALWAYS on the x-axis. • Distance is the dependent variable, and is ALWAYS on the y-axis.

  17. Velocity • Velocity – the SPEED and DIRECTION of an object. • Example: • An airplane moving North at 500 mph • A missile moving towards you at 200 m/s

  18. Question • What is the difference between speed and velocity? • Speed is just distance/time. Velocity includes direction as well.

  19. Velocity Problem • Indicate which of the following are velocities: • 125 cm/sec • 30 km/h northwest • 350m/sec north • 520 km/h

  20. Graphing Speed: Distance vs. Time Graphs Denver Phoenix

  21. Graphing Speed: Distance vs. Time Graphs Speed = Slope = Rise/Run Rise

  22. Graphing Speed: Distance vs. Time Graphs Speed = Slope = Rise/Run Rise=? 600 km 3 h

  23. Graphing Speed: Distance vs. Time Graphs Speed = Slope = Rise/Run Rise=? 600 m 3 minutes Rise/Run = 600 km/3 hr = 200 km/hr

  24. Different Slopes Slope = Rise/Run = 0 km/1 hr = 0 km/hr Rise = 2 km Run = 1 hr Rise = 0 km Run = 1 hr Slope = Rise/Run = 2 km/1 hr = 2 km/hr Rise = 1 km Run = 1 hr Slope = Rise/Run = 1 km/1 hr = 1 km/hr

  25. Question • Below is a distance vs. time graph of my position during a race. What was my AVERAGE speed for the entire race? Average Speed = Total distance/Total time = 12 km/6 hr = 2 km/hr Rise = 12 km Run = 6 hr

  26. Question • What does the slope of a distance vs. time graph show you about the motion of an object? • It tells you the SPEED

  27. Question • Below is a distance vs. time graph for 3 runners. Who is the fastest? Leroy is the fastest. He completed the race in 3 hours

  28. Acceleration • Acceleration = speeding up • Acceleration – the rate at which velocity changes • Can be an: • Increase in speed • Decrease in speed • Change in direction

  29. Types of acceleration • Increasing speed • Example: Car speeds up at green light • Decreasing speed • Example: Car slows down at stop light • Deceleration is when acceleration has a negative value. • Changing Direction • Example: Car takes turn (can be at constant speed) screeeeech

  30. Question • How can a car be accelerating if its speed is a constant 65 km/h? • If it is changing directions it is accelerating

  31. Calculating Acceleration • If an object is moving in a straight line • Units of acceleration: • m/s2

  32. Calculating Acceleration 1 s 2 s 3 s 4 s 0 s 4 m/s 12 m/s 16 m/s 0 m/s 8 m/s

  33. Question • A skydiver accelerates from 20 m/s to 40 m/s in 2 seconds. What is the skydiver’s average acceleration?

  34. A skateboarder is moving in a straight line at a speed of 3 m/s and comes to a stop in 2 sec. What is his acceleration?

  35. Graphing Acceleration • Can use 2 kinds of graphs • Speed vs. time • Distance vs. time

  36. Graphing Acceleration:Speed vs. Time Graphs • Speed is increasing with time = accelerating • Line is straight = acceleration is constant

  37. Graphing Acceleration:Speed vs. Time Graphs Rise = 4 m/s Run = 2 s • In Speed vs. Time graphs: • Acceleration = Rise/Run • = 4 m/s ÷ 2 s = 2 m/s2

  38. Graphing Acceleration:Distance vs. Time Graphs • On Distance vs. Time graphs a curved line means the object is accelerating. • Curved line also means your speed is increasing. Remember slope = speed.

  39. Question Run = 3 s Rise = -6 m/s Above is a graph showing the speed of a car over time. 1) How is the speed of the car changing (speeding up, Slowing down, or staying the same)? 2) What is this car’s acceleration? • The car is slowing down • Acceleration = rise/run = -6m/s ÷3s = -2 m/s2

  40. Question: The black and red lines represent a objects that are accelerating. Black is going a greater distance each second, so it must be speeding up. Red is going less each second, so must be slowing down Remember: in distance vs. time graphs: curved line = accelerating, flat line = constant speed • Which line represents an object that is accelerating?

  41. Question: Hard one Above is a graph showing the speed of a car over time. 1)What would a distance vs. time graph for this look like?

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