Lecture 2
EDUH 1017
Sports Mechanics
Lecture 2
Speed, distance and displacement
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Main Concepts
We need to build-up a basic vocabulary and set of tools
for discussing motion in a sporting context:
• Speed
• Distance-Time graphs
• Speed-Time graphs
• Average v. Instantaneous Speed
• Distance v. Displacement
• Speed v. Velocity
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Speed
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average speed =
distance travelled
time elapsed
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As an equation:
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SI Units are length/time – e.g. m/s or ms–1
sav = s =
l
t
(speed is always positive)
EDUH 1017 Sports Mechanics L2
How fast do they go?
• Human walking
• Human running
• Car
• Aircraft
• Sound
• Light
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Constant Speed
30 m/s
⎛
km ⎞
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hr ⎞
⎛
m⎞
m
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Distance-time graph
Constant or uniform speed – equal distances in equal times
EDUH 1017 Sports Mechanics L2
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EDUH 1017 Sports Mechanics L2
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110 km/hr
Example of conversion ⎜⎝ 110 hr ⎟⎠ × ⎜⎝ 3600 s ⎟⎠ × ⎜⎝ 1000 km ⎟⎠ ≈ 30 s
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Converting between units
“The distance travelled in a given amount of time”
Defined bit more carefully:
Average speed is the distance travelled (along any path)
divided by the time it took
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If speed (“rate-of-change
of distance”) is constant,
the distance-time graph is a
straight line
Slope of the line is the
ratio of the rise to the run
= a distance divided
by a time
= speed
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Distance-time graph
Often write Δ meaning
“change in”
so Δl = change in position
= (final position) –
(starting position)
Here
Δl = 30 m – 10 m
= 20 m
and
Δt = 3 s – 1 s
=2s
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Lines with different
slopes on a distancetime graph correspond
to different speeds
Greater slope means
faster moving
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Speed-time graph
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A horizontal line on a speedtime graph corresponds to
constant speed
The area under the curve
= speed × time
= distance travelled
(always, not just in this case)
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Instantaneous speed
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EDUH 1017 Sports Mechanics L2
EDUH 1017 Sports Mechanics L2
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Distance v. Displacement
How to specify the speed at an instant?
Narrow the time (∆t) of the average – geometrically this
comes closer and closer to the tangent to the curve
The slope of the tangent at P is the instantaneous speed
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The average speed over any part of a trip is the slope of the
line from the beginning to the end of that portion of the
distance-time curve
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Distance travelled is length along a path – has no direction
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Displacement is the straight line shift in position between
the end points – specifying length, but also direction
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Quite different for the
(walking/running?) turtle:
The distance he ran may be
20 cm, but his displacement
was only 10cm ~ North-East
He goes walking again, along
the light brown path.
Describe his path.
What distance did he walk?
Distance has a magnitude
(size) but no direction – it is
a scalar quantity
Displacement also has a
direction – a vector quantity
– represented by the arrow
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EDUH 1017 Sports Mechanics L2
What was his displacement?
In what direction?
Say he walked it in 10 s, what
was his speed?
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Velocity
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Speed has a magnitude (size) but no direction – it is a
scalar quantity – always positive
Velocity also has a direction – it is a vector quantity –
represented by an arrow – may be positive or negative
Average velocity is the displacement divided by the time it
d
took
v av =
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t
Units are length/time – e.g. m/s or ms–1
Vav vector is parallel to the d vector since t is just a scalar
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The average speed of the turtle
was
speed = distance/time
= 0.7 cm/s
The average velocity of the
turtle is
vav = displacement/time
= (5 cm NNE) / 10 s
= 0.5 cm/s NNE
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Summary
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Narrow the time (t) of the
average to get
instantaneous velocity –
geometrically this is the
tangent to the curve.
The bee has a fairly
constant speed, but the
velocity is changing
rapidly because the
direction is changing.
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EDUH 1017 Sports Mechanics L2
Main concepts:
• Difference between Distance and Displacement,
Speed and Velocity
• We can represent motion on distance (or
displacement) v. time graphs.
• Slope on a distance (or displacement) v. time graph is
speed (or velocity)
NEXT – describing motion using graphs
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