 Distance  Speed  Time *These are all scalar quantities -only magnitude  Displacement  Velocity  Acceleration *These are all vector quantities -magnitude and direction

DISTANCE  Total traveled  Path dependent  Scalar quantity  Both use the same variable and units  Variable: d (sometimes: x,r,ℓ)  Units: m DISPLACEMENT  Change in position  Path independent  Vector quantity

Check your understanding An odometer in your car shows: Distance

 The following is a list of gains and loses of a Bears possession  First down: gain 8 yards  Penalty lose 10 yards  Second down: gain 11 yards  Third down: lose 1 yard  What is the total distance?  What is the total displacement?

DIFFERENCES  Speed: how fast (scalar)  Always positive  Example: 25 m/s  Velocity: how fast in a certain direction (vector)  Can be positive or negative  Example: 25 m/s North SIMILARITIES  Variable: v  Units: m/s

Check your Understanding A speedometer in your car shows: Speed

Check your understanding Jim travels from Palatine to Chicago at 65 mph. Susie travels from Chicago to Palatine at 65 mph. Are the velocities equal? No, different directions

 v=(d f -d i )/(t f -t i ) OR commonly written as  v=∆d/ ∆ t *∆ means change Average Speed/Velocity

 In gym, you have to run the 100 m dash. If you run it in 18 s, what was your velocity?

 A freaky fast Jimmy Johns delivery man makes a delivery that is 2.2 miles away and it takes him 9 min. What is his average velocity in mi/hr?

SPEED (AVERAGE)  Total distance traveled divided by the total time elapsed **Example: Round trip drive to school VELOCITY  Total displacement divided by total time

 A change in velocity  Vector quantity  Positive vs. Negative Acceleration  + velocity and + acceleration = _____  + velocity and - acceleration = _____  - velocity and - acceleration = _____  - velocity and + acceleration = _____  Variable: a  Units: m/s/s or m/s 2  Equation: a=(v f -v i )/(t f -t i ) OR commonly written as: a= ∆v/ ∆ t

Check your understanding Name 3 ways to accelerate your car: 1. Step on gas pedal 2. Step on brake pedal 3. Turn steering wheel

 A car accelerates from a stop sign up to a speed of 11 m/s. If it takes 4 to do so, what is the car’s acceleration?

 Problem 1:  How long does it take a turtle to travel 1,000 m if it can travel at a pace of 1.3 m/s?  Problems 2:  What is the change in velocity if an object accelerates at 2 m/s 2 for 4.5 seconds?  If the object started at 3 m/s, what is its final speed?

DISTANCE VS. TIME GRAPHSVELOCITY VS. TIME GRAPHS  Slope is acceleration  Slope = rise/run = velocity/time = ACCELERATION  Area under graph is distance traveled  Area = base*height = velocity*time = Distance  Slope is velocity  Slope = rise/run = distance/time = Velocity

 Straight Lines – CONSTANT  Curving Lines – CHANGING  Flat Line - ZERO  Steeper the slope, the higher the value

 Definition of average velocity: (v i + v f )/2  Distance = rate * time: d=v avg *t  Definition of acceleration (final velocity): v f =v i + at  Timeless: v f 2 =v i 2 +2a∆d  Position: ∆d=v i t +1/2at 2

Equation∆xvivi vfvf ∆ta Definition of average velocity: v avg =(v i + v f )/2 Distance = rate * time: x=v avg *t √√√√○ Definition of acceleration (final velocity): v f =v i + at ○√√√√ Timeless: v f 2 =v i 2 +2a∆x √√√○√ Position: ∆x=v i t +1/2at 2 √√○√√

 Identify givens  Look for hidden givens  Identify unknown(s)  Compare givens and unknowns to equations  In the beginning: chart  Re-read problem if stuck *always show your work (G.U.E.S.S.)

 What is Starlin Castro’s acceleration as he runs toward first base if he reaches the base with a speed of 6.5 m/s? The distance between the plates is meters.

 An airplane can accelerate at a rate of 4.9m/s 2. If it takes 45 s for the plane to start to elevate and the plane starts from rest, what is the minimum length of runway required?

 Seeing a stop sign ahead, a person begins to brake as they drive lawfully on Cunningham. If their reaction time is 1 s, what is the total distance they need to stop if they can accelerate at -8 m/s 2 ?