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:

Some helpful distinctions:Distance is the amount of space between

two pointsPosition is the location of an object along a

real or imaginary line. Example: “at the 35 yard line” in a

football game

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?

DisplacementWhat 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.

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?

SpeedThe 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?

Instantaneous SpeedThis 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?

VelocityVelocity 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?

Average VelocityAverage Velocity

Average velocity is defined to be the Average velocity is defined to be the displacementdisplacement of an object divided of an object divided by the time elapsed.by the time elapsed.

Notice the difference from average Notice the difference from average speed?speed?

Average velocity vs. average speedAverage velocity vs. average speed

Think back to the bicycle Think back to the bicycle trip:trip:

3 km east, then 3 km west, 3 km east, then 3 km west, then 4 km east. If the whole then 4 km east. If the whole

trip took one hour, thentrip took one hour, thenWhat was your average What was your average

speed?speed?What was your average What was your average

velocity?velocity?

A futile endeavorA futile endeavor

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

AccelerationAcceleration

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

Positive and negative accelerationPositive and negative acceleration

Like velocity, acceleration is a Like velocity, acceleration is a VECTORVECTOR, meaning it has both a size , meaning it has both a size and a direction.and a direction.

A positive acceleration shows that A positive acceleration shows that velocity is increasing, while negative velocity is increasing, while negative acceleration shows velocity to be acceleration shows velocity to be decreasing.decreasing.

The sign of acceleration also shows The sign of acceleration also shows the direction the object is accelerating.the direction the object is accelerating.

Calculating accelerationCalculating acceleration

Acceleration = change of velocity Acceleration = change of velocity divided by time elapseddivided by time elapsed

a = a = v/tv/t

If a car goes from 20 km/hr to 40 If a car goes from 20 km/hr to 40 km/hr in five seconds, what is its km/hr in five seconds, what is its acceleration?acceleration?

Acceleration vectorsAcceleration vectors

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

Acceleration in an elevatorAcceleration in an elevator

Acceleration is something you can Acceleration is something you can feel. Think of an elevator:feel. Think of an elevator:– When you start at the bottom floor and When you start at the bottom floor and

the elevator speeds up upward, what is the elevator speeds up upward, what is the direction of the acceleration?the direction of the acceleration?

– How does that acceleration make you How does that acceleration make you feel?feel?

– When the elevator slows down at the When the elevator slows down at the top, what direction is it accelerating? top, what direction is it accelerating? How does that feel?How does that feel?