# Physics Question

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#### E_Reeves

##### Established Member
Hi all,

I had my last proper GCSE today, which was Physics. Most of the paper wasn't too bad, but I came across a question where I'm not sure if I'm incorrect or not...

The question: Driver C travels at 32m/s on the road and then stops. The car has a mass of 1200kg. Show kinetic energy stored at 32m/s is 614,000J.

I then do the calculation using the equation: kinetic energy = 1/2 x mass x velocity^2 and I got a result of 614,400J, not 614,000J. I'm not sure if I went wrong at all but some of my friends also noticed this too.

What are your thoughts on this?

Thanks R

#### gnolife

##### Established Member
Hi all,

I had my last proper GCSE today, which was Physics. Most of the paper wasn't too bad, but I came across a question where I'm not sure if I'm incorrect or not...

The question: Driver C travels at 32m/s on the road and then stops. The car has a mass of 1200kg. Show kinetic energy stored at 32m/s is 614,000J.

I then do the calculation using the equation: kinetic energy = 1/2 x mass x velocity^2 and I got a result of 614,400J, not 614,000J. I'm not sure if I went wrong at all but some of my friends also noticed this too.

What are your thoughts on this?

Thanks I seem to recall that the instructions on the front of the paper included that unless otherwise statied, answers were to be to 3 significant figures

I will add that I did my GCSEs in science 10 years ago now, so my statement may be outdated.

#### 433N

##### Guest
You are right ... and the paper should have been proof read to ensure that this kind of confusion could not arise.

(It is possible that they could argue that they are justified in stating the answer as 614000 on the grounds of significant figures but at no point in the question is this specified or implied implicitly - unless there was some statement to the effect that all figures are to 3 significant figures on the front of the paper or something - but then 32 should be 32.0 : ON EDIT - written before the above post. I would still argue that writing 32 is accurate to 3 significant figures is a nonsense).

This sort of thing happens far too often these days ... too little scrutiny at the time the paper was prepared.

#### E_Reeves

##### Established Member
You are right ... and the paper should have been proof read to ensure that this kind of confusion could not arise.

(It is possible that they could argue that they are justified in stating the answer as 614000 on the grounds of significant figures but at no point in the question is this specified or implied implicitly - unless there was some statement to the effect that all figures are to 3 significant figures on the front of the paper or something - but then 32 should be 32.0 : ON EDIT - written before the above post. I would still argue that writing 32 is accurate to 3 significant figures is a nonsense).

This sort of thing happens far too often these days ... too little scrutiny at the time the paper was prepared.
It's not the first mistake in these exam series as well. There have been a few others but luckily they were identified by the exam board and they sent out an erratum notice for it. It should not happen, especially considering the amount of time they've had to prepare this exam...

I don't recall seeing anything about significant figures on the front of the paper.

#### SS4

##### Established Member
The question: Driver C travels at 32m/s on the road and then stops. The car has a mass of 1200kg. Show kinetic energy stored at 32m/s is 614,000J.
Your answer is correct and as far as I can tell it comes down to significant figures - in a calculation you should always round your answers to the least precise value. However, if this were the case here you'd have 610,000 as both mass and velocity are 2 significant figures.

No doubt it's a poorly written question though - it should never be merely assumed that 3sf is the correct rounding

#### E_Reeves

##### Established Member
I did put ~614,000 after my calculation though so hopefully I'll get the mark. I should definitely get the mark for using the correct equation anyway, but there's not much I can do about it now, I suppose.

#### 433N

##### Guest
Your answer is correct and as far as I can tell it comes down to significant figures - in a calculation you should always round your answers to the least precise value. However, if this were the case here you'd have 610,000 as both mass and velocity are 2 significant figures.
To be fair, we don't know how many significant figures the mass is accurate to but, like you, I would assume that the velocity is accurate to 2 sig figs which would limit the accuracy of the answer to 610,000 ( 2 s.f.) .

Unfortunately, at almost every level including university, significant figures and accuracy are introduced and it is stressed how important they are. Then the person introducing them will lazily use arbitrary numbers (often 10 minutes after introduction) with no regard for them. The use of sig figs requires extremely careful (pedantic, even) thought and few have the rigour or self-discipline (or nerdocity) to use them correctly and consistently.

#### E_Reeves

##### Established Member
We were taught to put the full answer unless the question said to do otherwise. If there were many decimal numbers then I'd round to 2 decimal places, but I wouldn't personally use SF unless told to specifically.

#### TheNewNo2

##### Member
Your answer of 614,400 is correct. As stated by others, the issue is likely that the question is applying a rounding without stating so explicitly, which is on them. If we assume the mass is accurate, then their 614,000 value gives a speed of 31.98958 m/s, which is 32m/s to 5sf.

I would say that this is why you should study pure maths - they stop asking you to show things to a certain number of decimal places and instead just tell you to prove something, and the answer will usually be expressed in terms of Pi.

#### 433N

##### Guest
... or a surd.

You know when you're getting serious in maths when you're not allowed a calculator in the exam. Strangely, many people think Maths is all about numbers. #### D365

##### Established Member
We were taught to put the full answer unless the question said to do otherwise. If there were many decimal numbers then I'd round to 2 decimal places, but I wouldn't personally use SF unless told to specifically.
Trouble is, they either state the 3SF on the front page, or not at all, and rely upon the teacher to point this out.

#### aformeruser

##### Veteran Member
(It is possible that they could argue that they are justified in stating the answer as 614000 on the grounds of significant figures but at no point in the question is this specified or implied implicitly - unless there was some statement to the effect that all figures are to 3 significant figures on the front of the paper or something - but then 32 should be 32.0 : ON EDIT - written before the above post. I would still argue that writing 32 is accurate to 3 significant figures is a nonsense).
I have a vague memory of Physics A Level saying to give all answers to 3 significant figures unless otherwise stated, while the Mechanics part of Maths said to 1 decimal place unless otherwise stated, meaning if you were asked for the force of gravity on a Physics paper you would say 9.81 m/s squared, but on the Maths paper you would say 9.8.

If that is still the case and the question just said "Find the kinetic energy stored at 32m/s" you would give the answer to 3 significant figures and I would have given it in KJ unless stated but it is stated to give the answer in J.

#### amateur

##### On Moderation
... or a surd.

You know when you're getting serious in maths when you're not allowed a calculator in the exam. Strangely, many people think Maths is all about numbers. Wait until you have to study pure maths!

#### 433N

##### Guest
Wait until you have to study pure maths! I already have a degree in Maths (well joint Maths and Physics so I guess that I've pretty much done with my Pure Maths - my degree was mainly Applied).

I was being facetious ... I've even done quite a bit of numerical analysis and I'm pencilled in for some more on a Masters I've signed up for.

#### DarloRich

##### Veteran Member
Hi all,

I had my last proper GCSE today, which was Physics. Most of the paper wasn't too bad, but I came across a question where I'm not sure if I'm incorrect or not...

The question: Driver C travels at 32m/s on the road and then stops. The car has a mass of 1200kg. Show kinetic energy stored at 32m/s is 614,000J.

I then do the calculation using the equation: kinetic energy = 1/2 x mass x velocity^2 and I got a result of 614,400J, not 614,000J. I'm not sure if I went wrong at all but some of my friends also noticed this too.

What are your thoughts on this?

Thanks My thoughts are that this has reinforced why I stopped having anything to do with maths after my GCSE exams which were about 400 years ago! Is to possible to have this explained in English? #### edwin_m

##### Veteran Member
My thoughts are that this has reinforced why I stopped having anything to do with maths after my GCSE exams which were about 400 years ago! Is to possible to have this explained in English? Surely you don't expect the English teacher to understand maths?

#### amateur

##### On Moderation I already have a degree in Maths (well joint Maths and Physics so I guess that I've pretty much done with my Pure Maths - my degree was mainly Applied).

I was being facetious ... I've even done quite a bit of numerical analysis and I'm pencilled in for some more on a Masters I've signed up for.
Group theory, number theory, topology, proofs ....they never told you about that at GCSE or a levels

#### PeterC

##### Established Member
After school I found degree level maths a foreign language and got a job in finance instead where I was dealing with real numbers. I ended up with a degree in geography and a career in computing and now dabble in music journalism.

#### DynamicSpirit

##### Established Member
Your answer is correct and as far as I can tell it comes down to significant figures - in a calculation you should always round your answers to the least precise value. However, if this were the case here you'd have 610,000 as both mass and velocity are 2 significant figures.

No doubt it's a poorly written question though - it should never be merely assumed that 3sf is the correct rounding
I think this is the correct analysis. In this case, if the speed was given as 32m/s then that implies only two significant figures, so the answer cannot be given to more than 2 significant figures. Giving the mass as 1200kg seems like rather bad practice, because it's ambiguous how many significant figures are intended - two or four - but this doesn't impact on the answer when speed is already limited to 2 significant figures.

If the paper really did say exactly what E_Reeves has quoted, then a complaint to the examining board would seem warranted (but I'd probably want to confirm that's exactly what the paper said first).

#### E_Reeves

##### Established Member
I think this is the correct analysis. In this case, if the speed was given as 32m/s then that implies only two significant figures, so the answer cannot be given to more than 2 significant figures. Giving the mass as 1200kg seems like rather bad practice, because it's ambiguous how many significant figures are intended - two or four - but this doesn't impact on the answer when speed is already limited to 2 significant figures.

If the paper really did say exactly what E_Reeves has quoted, then a complaint to the examining board would seem warranted (but I'd probably want to confirm that's exactly what the paper said first).
I wrote it down in the exam on scrap paper, so I'm sure it's correct. I can ask to see the paper at school anyway, so I might look again

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