Some helpful distinctions:

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 cars 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?