Learning Target 3: Velocity
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3.1 I can calculate speed and velocity3.2 I can distinguish between speed and velocity3.3 I can use a graph to determine and describe motion velocity, and other elements of the graph
Learning Target 3: Velocity
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Why?? Motion happens all around us
Cars, people, soccer balls, etc. How do we begin to see and analyze
motion as an engineer does?
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What is motion? Motion: change of the position of an
object with respect to time
Ouch.
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Definition: Total length traveled
What distance did the turtle cover?
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Definition: change in the position of an object from its beginning point
Formula: Δx = xf-xi
Δxxi
xf
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Displacement = change in position from start Distance = total length traveled
What total distance did the turtle cover? What was his displacement?
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Displacement Positive displacement: moving up or
forward
Negative displacement: moving down or backward
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Quick Checks What is the difference between distance
and displacement? What letter do we use to represent
position?
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Quick Checks
2 m
4 m
2 m
4 m
+
+
-
-
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Speed Definition: rate of change in distance
with respect to time
Formula: speed = distance/time
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Definition: rate of change in displacement with respect to time
Formula: vavg = xf – xi = displacement = d tf – ti time t
Units: length/time
Average Velocity
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Average Velocity Can be positive or negative
Depends on sign of displacement Positive velocity = moving forward Negative velocity = moving backward
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Velocity vs. Speed Velocity is a VECTOR quantity, which
means it describes motion with both magnitude and direction Rate of change of DISPLACEMENT with
respect to time Speed is a SCALAR quantity, which
means it has no direction, only magnitude Rate of change of DISTANCE with respect to
time
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What is Measured?
Units Symbol
Time s, min, hours t
Distance m, km,cmmi, ft, in
d
Displacement m, km,cmmi, ft, in
d
Velocity m/s, km/hrmph
v
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Quick Checks What is the difference between speed
and velocity? What is the equation for average
velocity? What does it mean for motion when
velocity is positive? Units for time? Distance? Displacement?
Velocity?
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The GUESS Method During football practice, Martin and Jesus
run 2.7 miles eastward in 25 minutes. How fast were they running?
GivenUnknownEquationSubstitute Solve
2.7 miles = d, 25 minutes = t velocity
v = d/tv = 2.7 miles/25 minutes
v = 0.108 miles/min
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Position vs. Time GraphsWhat is in a position vs. time graph? X-axis: time (s) that the object is in
motion Y-axis: position (m) of the object in
motion SLOPE of the line = velocity!
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How to Find Slope Slope = rise = Δy
run Δx = How much your position is changing
How much your time is changing
sloperiserun
yx
positiontime
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Position vs. Time
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What is the velocity between t = 0 and t = 4?
Slope = Δy/ΔxSlope = 20m/4 s = 5 m/s
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What is the velocity between t =4 and t = 6?Slope = Δy/ΔxSlope = 0m/2 s = 0 m/sWhen an object is at rest, its velocity = 0 so slope =
0
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What is the velocity between t = 6 and t = 8?
Slope = Δy/ΔxSlope = 20m/2 s = 10 m/s
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What is the velocity between t = 8 and t = 12?Slope = Δy/ΔxSlope = -20m/4 s = -5 m/sNegative velocity means…?
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20 40
The steeper the line, the higher the velocity = faster the object is moving
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The steeper the line, the higher the velocity = faster the object is moving
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Exit Ticket
On a scrap piece of paper, answer the following
questions about the graph
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Exit Ticket
Look at the graph. It shows how 3 runners ran a 100-meter race.1.Which runner won the race?2.Which runner stopped for a rest?3.How long did he stop to rest?4.How long did Ron take to complete the race?5.What is David’s average speed?
0 2 4 6 8 10 12 14 16 18
David Ron Beckham
Time (s)
Posi
tion
(m
)