Speed, Distance and Time /

Unit Conversions

 

 

SPEED, DISTANCE, TIME

 

So you’re walking down a crowded sidewalk – are you passing people or being passed, etc.

 

?? How fast do you think you walk normally? What would be a slow value? A fast “pace”?

 

“I walk at 5.”

“5 what?”

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

 

We’ll talk about units more later but, for now, we’ll stick to feet, meters, and seconds for the experiment we’re 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 “RATE” (as in “Velocity”...)

 

?? So let’s say you ran 8 miles in an hour – how fast did you run?

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

 

SPEED = DISTANCE / TIME !!!!

 

?? How long does it take you to drive 120 miles if you’re going 60 MPH?

-      How long to go 30 miles?

 

TIME = DISTANCE / SPEED !!!!                                d

                                                      ______________

Here’s 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 – your typical speed.

 

Let’s 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 same… (*** WE’LL 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 “normal” pace both times they should be, right? How can we check that we got the same speed in both cases? We need to “convert” them to the same UNITS so we can compare “apples with apples”

 

Your number, the “answer” to how fast you walk depends on your “UNITS”

but its all still the same type of thing – a “Speed”, in this case

 

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

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

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

 

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

ANOTHER WAY TO LOOK AT IT – THERE”S MORE THAN ONE “ANSWER” DEPENDING ON THE UNITS YOU USE BUT THEY REPRESENT THE SAME THING PHYSICALLY, IE THE SAME “REAL” THING.

 

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

 

BUT IT ALL MEANS THE SAME THING –

- I can break a boat’s 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 car’s speed up into m/s or MPH

 

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

it’s called “UNIT CONVERSION”

 

Other examples?

 

Let’s do some more that you’ll use a lot:

 

?? How long is a meter? – 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? – is a 1600 meter race same as running the mile?)

 

Too hard? – 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 – THEY CANCEL OUT WHEN YOU HAVE IT APPEARING IN THE NUMERATOR AND THE DENOMINATOR.