Try this one.

Dr Who trots gently round a 400 m oval track at an average speed of 2 m/s At what speed must he run a second lap to average 5 m/s over the full 800 m?

(A clue to the answer is in the character)


The answer is 8 m/s.

If you run at a speed of 2 m/s in the first lap, then x becomes the speed in the second lap. The average speed is the first lap plus the second lap divided by 2. The speed in the second lap is unknown, so it becomes x. The formula is: 0.5(2+x)=5. Thus x = 8


You have to know how to do algebra Steve if you want to get the answer. Most imperial users have trouble setting up equations and people in imperial countries have the worse math scores. I wonder why that is.

Hmm

Do these three calculations and see what you make of it:

(i) How long does it take to do the first lap at 2 m/s

(ii) How long would it take to do the second lap at 8 m/s

(ii) Ignoring how fast actually runs at any particular time, how long would it take to run 800 m at an average speed of 5 m/s.

(for simplicity just leave your answers in seconds)

Hmm

Do these three calculations and see what you make of it:

(i) How long does it take to do the first lap at 2 m/s

400 m x 1 s/2 m = 200 s


(ii) How long would it take to do the second lap at 8 m/s

400 m x 1 s/8 m = 50 s

(ii) Ignoring how fast actually runs at any particular time, how long would it take to run 800 m at an average speed of 5 m/s.

800 m x 1 s/5 s = 160 s

(for simplicity just leave your answers in seconds)

250 s does not equal 160 s.


Actually the answer is correct. You're not looking to achieve the same times. You're asking for average speeds. Running at 2 m/s in the first lap and 8 m/s in the second averages 5 m/s over the total. Running an average speed over 800 m in which two equal segments have different speeds, is not he same effect as running an average speed of 5 m/s over the full 800 m length. Think about it. It does make sense.

So if you were given only the total time taken and the overall distance would you not be able to calculate average speed? Would you require a profile of the speed travelled at every point on the journey?

I guess it comes done what do we really mean by average speed. The usual notion as I understand is that of the equivalent constant speed that would cover the distance in the same time.

Now you may say that this latter definition doesn't relate to any form of average, i.e. arithmetic mean (total of a series of values divided by the number of those values). Actually it does but to show this I'll give you a clue in the next problem:

A runner goes twice round a 400 m track. He starts off at 2 m/s and maintains that for 80 s at which point he accelerates to 8 m/s and maintians that speed till the end.

(i) How long does he spend running at 8 m/s?

(ii) What is the average speed?

(iii) What speed do you get if you divide 400 m by the overall lap time.

Sorry, strike the part (iii) question and replace it with:

(iii) What speed do you get if you divide 800 m by the overall time taken?

At last the episode of Dr Who on Saturday has gone back to the original format of having the cliff-hanger at the end before the scream of the end credit music.

Good Stuff.

(Oh, and it was all in imperial again)

I dunno Steve. I watched the first one, but somehow, can't put my finger on it, it just didn't work for me.

I thinks it's because the man came across as too ordinary. In spite fo all the modern special effects it just didn't create any sense of drama.

I don't know why they keep trying to revive it. They'd be better off creating something completely different, something original. There are plenty of good sci-fi writers around who would do something for them.

Steve

(Oh, and it was all in imperial again)

He is a very old man. 900 years I believe!!!!

Are we all looking forward to the thrilling episode where Billie Piper prevents the Daleks from enforcing metre sticks on Edward I.

"Doctor, these evil foreigniers are using brain control to make Edward I change the length of his Ulna"

Scream!!!!!!!....... Doo eee oooh, dee dee oooooooh...........

Berengexterminate:

"He is a very old man. 900 years I believe!!!! "

Keep with the times, man! Two weeks ago he went forward 30,000 years! (Maybe the "year" will be replaced by the ZotoDay by then!!)

"Are we all looking forward to the thrilling episode where Billie Piper prevents the Daleks from enforcing metre sticks on Edward I."

Don't diss the daleks, mate! They can get up staircases now you know!!

<<"Doctor, these evil foreigniers are using brain control to make Edward I change the length of his Ulna"
Scream!!!!!!!....... Doo eee oooh, dee dee oooooooh...........>>


THAT'S the sort of cliff-hanger noise/moment I'm on about! Thanks for transcribing it into type!

Stan: Do you dislike the New Doctor because of the numerous usages of imperial on a drama-series that's aimed at very young people (behind the sofa) as well as us adult-types (behind the cupboard)?

Hmmm?

I suspect his Tardis was ACTUALLY spec'd in metric and converted to imperial "as an afterthought". You know, a bit like vinyl records and london marathons!

;-)

How does the Macdonalds Ad go? "I'm luvvin it" !!

:-D

SteveH:
"Stan: Do you dislike the New Doctor because of the numerous usages of imperial on a drama-series that's aimed at very young people (behind the sofa) as well as us adult-types (behind the cupboard)?"

Stan:
Not really. It's no more than I'd expect from the BBC anyway. I couldn't give a monkeys.

Give it a few more episodes and they'll drop it again like they always do.

BTW if you're only reason for watching it is to come up for air from that sea of suffocating metric ...

Well who can blame you.

<<Give it a few more episodes and they'll drop it again like they always do>>

Is that why they have the next Doctor lined up already?

BTW - miles, feet and inches were used in last night's episode.

It's not a critical thing, but using imperial instead of metric gives the programme a less "political" feel. It's more down to earth and aimed at British people. I bet it'll go down well in the US when it gets aired there too.

Question is, in Europe will they do subtitles (or dub) in metric converted or stick with imperial?

SOmething tells me a certain someone will know the answer to that catagorically without a shred of evidence!!! ;-)