distance speed time *these are all scalar quantities -only magnitude displacement velocity ...
TRANSCRIPT
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
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
A speedometer in your car shows:
Speed
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=(df-di)/(tf-ti)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/s2
Equation:a=(vf-vi)/(tf-ti)
OR commonly written as:
a= ∆v/ ∆ t
Name 3 ways to accelerate your car:1.Step on gas pedal2.Step on brake pedal3.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/s2 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 – CONSTANTCurving Lines – CHANGINGFlat Line - ZERO
Steeper the slope, the higher the value
Definition of average velocity: (vi + vf)/2
Distance = rate * time: d=vavg*t
Definition of acceleration (final velocity): vf=vi + at
Timeless: vf
2=vi2 +2a∆d
Position: ∆d=vit +1/2at2
Equation ∆x vi vf ∆t a
Definition of average velocity: vavg=(vi + vf)/2
Distance = rate * time:x=vavg*t √ √ √ √ ○
Definition of acceleration (final velocity): vf=vi + at
○ √ √ √ √
Timeless:vf
2=vi2 +2a∆x √ √ √ ○ √
Position:∆x=vit +1/2at2 √ √ ○ √ √
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 27.432 meters .
An airplane can accelerate at a rate of 4.9m/s2. 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/s2?