Sem 2, 2014 EDUH 1017 Sports Mechanics L2 1

EDUH 1017Sports Mechanics

Lecture 2Speed, distance and displacement

Sem 2, 2014 EDUH 1017 Sports Mechanics L2 2

Lecture 2

Main ConceptsWe need to build-up a basic vocabulary and set of toolsfor 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

• “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

• As an equation: (speed is always positive)

• SI Units are length/time – e.g. m/s or ms–1

average speed =

distance travelledtime elapsed

�

sav = s = lt

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Converting between units

How fast do they go?• Human walking• Human running• Car 30 m/s 110 km/hr• Aircraft• Sound• Light

• Example of conversion 110kmhr

⎛⎝⎜

⎞⎠⎟×

13600

hrs

⎛⎝⎜

⎞⎠⎟× 1000 m

km⎛⎝⎜

⎞⎠⎟≈ 30 m

s

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Constant Speed

• Constant or uniform speed – equal distances in equal times

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Distance-time graph

• 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 mand Δt = 3 s – 1 s = 2 s

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• Lines with different slopes on a distance-time graph correspond to different speeds

• Greater slope means faster moving

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Speed-time graph

• A horizontal line on a speed-time graph corresponds to constant speed

• The area under the curve= speed × time= distance travelled(always, not just in this case)

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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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Instantaneous speed

• 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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Distance v. Displacement

• Distance travelled is length along a path – has no direction

• 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

• 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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He goes walking again, along the light brown path.

Describe his path.

What distance did he walk?

What was his displacement?

In what direction?

Say he walked it in 10 s, what was his speed?

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Velocity

• 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 took

• 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

vav =

dt

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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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• 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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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

Summary