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Some helpful distinctions:

Some helpful distinctions:. Distance is the amount of space between two points Position is the location of an object along a real or imaginary line. Example: “at the 35 yard line” in a football game.

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Some helpful distinctions:

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  1. Some helpful distinctions: • Distance is the amount of space between two points • Position is the location of an object along a real or imaginary line. • Example: “at the 35 yard line” in a football game

  2. Displacement is the difference in position an object undergoes when it moves. Roughly speaking, it is like the distance covered by a moving object. • Displacement is calculated from the difference of two positions along a line. • What is the displacement of the football when it is thrown from the 50 yard line to the 80 yard line?

  3. Displacement • What is the displacement of the ball when it is thrown backward from the 50 yard line to the 30 yard line? • A negative displacement shows that position is decreasing. • The sign would be opposite if you were numbering the field from the opposite end.

  4. A story problem • Biking your way to school from Victoria, you travel three km east, then realize that you left your scientific calculator at home. You return home, then proceed four kilometers east to get to CHS. • What was the total distance you traveled? • What was your displacement, from start to finish?

  5. Speed • The average speed an object travels is equal to the distance it covers divided by the time elapsed. • What is the average speed of an athlete who completes a 100 meter race in ten seconds? • Did the athlete likely run 10 meters in the very first second after starting? What about the last second?

  6. Instantaneous Speed • This is the speed an object is traveling right at some instant. • If a car has an average speed of 60 miles per hour while on a trip to Duluth, does that mean that the car’s instantaneous speed must be 60 mph when it passes Hinckley? • An object is moving at a constant speed of 20 m/s for five seconds. What is its average speed during that time?

  7. Velocity • Velocity is speed in a given direction, like “thirty meters per second north”. • If the direction changes, the velocity does too! • How is it possible for an object to have a changing velocity while moving at a constant speed?

  8. Average Velocity • Average velocity is defined to be the displacement of an object divided by the time elapsed. • Notice the difference from average speed?

  9. Average velocity vs. average speed Think back to the bicycle trip: 3 km east, then 3 km west, then 4 km east. If the whole trip took one hour, then What was your average speed? What was your average velocity?

  10. A futile endeavor • Formula 1 race cars can hit speeds over 200 mph. If these racers average speeds of 170 mph on straight stretches and 120 mph on curves, what do you think their average velocity would be on one complete circuit of a track?

  11. Acceleration • Acceleration is how fast the velocity of an object is changing. • If a car can go from zero to 60 mph in five seconds, about how much does its velocity increase in each second? • Its acceleration would be “twelve miles per hour per second”, or 12 mi/hr/s

  12. Positive and negative acceleration • Like velocity, acceleration is a VECTOR, meaning it has both a size and a direction. • A positive acceleration shows that velocity is increasing, while negative acceleration shows velocity to be decreasing. • The sign of acceleration also shows the direction the object is accelerating.

  13. Calculating acceleration • Acceleration = change of velocity divided by time elapsed • a = v/t • If a car goes from 20 km/hr to 40 km/hr in five seconds, what is its acceleration?

  14. Acceleration vectors • You are backing up in your car at a speed of three meters per second. Three seconds later, your car is moving forward at a speed of six meters per second. What is the size (magnitude) and direction of your average acceleration?

  15. Acceleration in an elevator • Acceleration is something you can feel. Think of an elevator: • When you start at the bottom floor and the elevator speeds up upward, what is the direction of the acceleration? • How does that acceleration make you feel? • When the elevator slows down at the top, what direction is it accelerating? How does that feel?

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