Graphs of &quot;Distance From&quot; against time

Discussion in 'Mathematics' started by begbiesan, Mar 21, 2011.

1. begbiesan

<img alt=" />Am I missing something vital?
I see distance-time graph questions frequently: in text books, and in exams.
The y-axis represents "distance from" somewhere. Eg. Edexcel Specimen Higher Paper 3
http://www.edexcel.com/migrationdocuments/Current%20GCSE/320326_Unit_3_Higher_section_A_Nov_2007.pdf<img alt=" /><img alt=" /><img alt=" />
Sian travels to a shop and home again. There is a marvellous representation of a travel graph.
We all know what the graph is MEANT to represent, but there are many interpretations, aren't there, other than the supposed 'correct' answer?
Why are the graphs not more accurately defined?
In the above question, the answer to the first part is expected to be 8km in 10mins is 48km/h.
But what if this journey was on a road spiralling away from her house, and she'd actually covered 20km to reach a position 8km from her home?
Half an hour into her journey, we are expected to say that Sian is stationary at the shop for 15 minutes. An equally likely situation is that she is on the ring road for 15 minutes, maintaining a distance of 20km from her house. Who knows what her speed is at this time?
Finally, to complete the travel graph, I could draw ANY of several different lines, straight or otherwise and argue that each could fulfill correctly the specified 60km/h requirement.

2. FlippantFlyer

I don't see a problem with it really other than to qualify the question by saying that the distances are along the direction of travel. However I would suggest that is superfluous as when we look at distances on maps for walking or driving purposes we are more interested in actual distances covered along the route. An exception might be orienteering perhaps, where you might cover the distance as the crow flies.

3. siddons_sara

IMO the objections of the OP are entirely valid. In addition, Siân might well have travelled home by a different route, making a wide variety of answers possible to the second part.

4. FlippantFlyer

Well if she travelled home by a different route which was longer or shorter, then we would not have been able to use that travel graph to complete the journey. The graph clearly states she was 20 km from home so there can only be one line to show the answer. However you could argue that the return speed should have been qualified by being a constant speed from the point she left the shop until the instant she arrived home, otherwise it would not be a straight line. Suddenly we are left with the possibility of half a page of text to completely specify the question! The OP has already said that they know what is meant by the question. I think we need to look at the question intuitively in the context that it is set.

5. Maths_MikeNew commenter

The distance is a scalar quantity. The direction of travel is irrelevant. She migth have soent 10 minutes going round in circles this would not matter.

Think of a car it records distance travelled - regardless.

(I think you are confusing it with displacement - as used in kinematics)

And in general you are trying to unnecessarily complicate what is (and rightly so) a simple concept.

6. Maths_MikeNew commenter

Oh I see - i actually argue in favour of the OP!!!

Just because the shop is 20km from home does not necessarily mean (and in fact it is not likley to be the case) - that she would travel 20km to get there and it is equally unlikely she would do the exact same distance on the way home.

7. Maths_MikeNew commenter

So a much better question would refer to the distance travelled rather than how far the shop is away from home.

I.e A person travelled a distance of 8 km for her home to a shop. On the way home she travelled the same distance.

etc

8. FlippantFlyer

Yeah, thanks for sorting all that out for us Mike!
ROFL

9. siddons_sara

Apology accepted FlippantFlyer and please accept my apology for being a bit snappy back!

TES is the first forum I've written on and didn't really think it through before putting my picture there. It was only when I started writing and realised that most people don't put a picture or use a graphic that I thought again but couldn't be fussed to change!