__Speed, Distance and
Time /__

__Unit Conversions__

**SPEED, DISTANCE, TIME**

So youÕre walking down a crowded sidewalk Ð are you passing people or being passed, etc.

**??
**How fast do
you think you walk normally? What would be a slow value? A fast ÒpaceÓ?

ÒI walk at 5.Ó

Ò5 what?Ó

You need to specify 5 of what, that is UNITS, in this case MPH

WeÕll talk about units more later but, for now, weÕll stick to feet, meters, and seconds for the experiment weÕre going to do.

**??** You go out for a jog.

- If you ran at a constant 10 MPH for 1 hour, how far have you gone?

How did you know that?

- 10 MPH still but for ½ hour only (half as long)?

How did you know that?

** DISTANCE
= SPEED * TIME**
!!!! d for DISTANCE

t for TIME

v
for SPEED or ÒRATEÓ (as in Ò** V**elocityÓ...)

**??** So letÕs say you ran 8
miles in an hour Ð how fast did you run?

- How about 8 miles in 2 hours Ð how fast did you run?

** SPEED
= DISTANCE / TIME**
!!!!

**??** How long does it take you
to drive 120 miles if youÕre going 60 MPH?

- How long to go 30 miles?

** TIME
= DISTANCE / SPEED** !!!! d

______________

HereÕs how to remember these equations:

v t

**PRE-EXPERIMENT**

**??** So how might you design an
experiment to find out your own personal walking speed?

**(LET
THE GROUP COME UP WITH THE ANSWER....)**

**??** Now, do you think you walk
exactly the same speed each time? If not, how might you correct for this? This
could be called your *average* walking speed Ð your typical speed.

LetÕs try feet and then meters so that we can use different units and see if the answers, once we convert both to MPH, come out the sameÉ (*** WEÕLL EXPLAIN HOW TO DO THIS AFTER THE EXPERIMENT IS PERFORMED.)

*****
HAND OUT DATASHEET**

So
now take a moment to *predict* how fast you walk in m/s? in ft/s?

**WRITE
IT ON THE DATASHEET!**

**ENSURE
THE PROCEDURES THE GROUP HAS AGREED UPON ARE CLEARLY OUTLINED BEFORE GOING
OUTSIDE**

** Will need (1 ea per group * about 10 groups):

- 50 ft string

- 5 m string

- stop watch

- clipboard

**UNIT CONVERSION**

**(post-experiment)**

So now we have long it took to walk 50 feet and how long it took to walk 30 meters.

In both cases, was your speed the same? If you walked at your ÒnormalÓ pace both times they should be, right? How can we check that we got the same speed in both cases? We need to ÒconvertÓ them to the same UNITS so we can compare Òapples with applesÓ

Your number, the ÒanswerÓ to how fast you walk depends on your ÒUNITSÓ

but its all still the same **type** of thing Ð a ÒSpeedÓ, in this case

e.g. I could say I have 10 gallons of milk or 40 quarts Ð same thing.

I could say I held my breath for 1 minute or 60 seconds Ð same thing.

I could say I am 6 feet tall or 72 inches tall Ð same thing.

YOUR ANSWER Ð THE ACTUAL NUMBER - DEPENDS ON THE UNITS YOU CHOOSE

ANOTHER WAY TO LOOK AT IT Ð THEREÓS MORE THAN ONE ÒANSWERÓ DEPENDING ON THE UNITS YOU USE BUT THEY REPRESENT THE SAME THING PHYSICALLY, IE THE SAME ÒREALÓ THING.

SO THAT MEANS YOU NEED TO PUT UNITS WITH YOUR NUMBER Ð DO YOU MEAN MPH OR m/s?

BUT IT ALL MEANS THE SAME THING Ð

- I can break a boatÕs length into chunks a foot long or a meter long

- I can break a certain length of time into seconds or minutes

- I can break a carÕs speed up into m/s or MPH

When I convert 1 minute into 60 seconds or 1 foot into .3048 meters

itÕs called ÒUNIT CONVERSIONÓ

Other examples?

LetÕs do some more that youÕll use a lot:

**??** How long is a meter? Ð i.e.
is it |<----------- this long? ---------->|

- How many feet in a meter?

- How many feet in a mile? (any runners?)

- So then how many meters in a mile? How did you do that?

5280 ft/mile / .3048 meters/ft = 1609 meters/mile

(any runners? Ð is a 1600 meter race same as running the mile?)

Too hard? Ð Try this:

- How many inches in a foot? How many feet in a yard?

Therefore, how many inches in a yard? How did you do that?

12 in/ft * 3 ft/yd = 36 in/yd

Another: How many seconds in a minute?

How many minutes in an hour?

So then how many seconds in an hour?

Then how many seconds in a day? In a year?

60 s/min * 60 min/hr * 24 hr/day * 365 day/yr = 31,536,000 s/yr

SO THEN UNITS WORK JUST LIKE VARIABLES Ð THEY CANCEL OUT WHEN YOU HAVE IT APPEARING IN THE NUMERATOR AND THE DENOMINATOR.