Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 317

BBC Bitesize (Acceleration)

When referring to speed on this page they often say things like,

“The bus has a constant speed of 10ms-¹"

I've not seen this before. I'm used to seeing speed given as simply, for example, 10m/s

Why the -¹ ?

I've noticed also for acceleration instead of saying, 10m/s/s, or 10m/s², they write 10m s -². Why might they do this?

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Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,422

Re: BBC Bitesize (Acceleration)

Velocity or speed is given by m/s (meters per second) and Acceleration is given in Meters per second squared.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 240

Re: BBC Bitesize (Acceleration)

I guess you know that x^m/x^n = x^(m-n)
Therefore, x^a/x^a = 1 = x^0, x could be any number.

Now we can write:
1/s = s^0/s^1 = s^(0-1) = s^-1 ===> s-¹
Similarly,
1/s^2 = s^0/s^2 = s^(0-2) = s^-2 ===> s-²

Last edited by KerimF (2024-09-19 00:08:24)

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Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

paulb203

Member

Registered: 2023-02-24

Posts: 317

Re: BBC Bitesize (Acceleration)

Velocity or speed is given by m/s (meters per second) and Acceleration is given in Meters per second squared.

.

Thanks, Jai Ganesh.

Why does ms^-2 give velocity?

ms^-2
= m x (1/s^2), yeah?
= m/s^2, yeah?
= m/(s x s), yeah?

If I've got that right, why does m/(s x s) give velocity?

I thought velocity was simply, for example, 10m/s downwards, or 30mph East, etc?

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Prioritise. Persevere. No pain, no gain.

paulb203

Member

Registered: 2023-02-24

Posts: 317

Re: BBC Bitesize (Acceleration)

I guess you know that x^m/x^n = x^(m-n)
Therefore, x^a/x^a = 1 = x^0, x could be any number.

Now we can write:
1/s = s^0/s^1 = s^(0-1) = s^-1 ===> s-¹
Similarly,
1/s^2 = s^0/s^2 = s^(0-2) = s^-2 ===> s-²

Thanks, KerimF

A very helpful explanation. I think I've followed all of that.

But I think my problem is how I see the term, "metres per second".

Although I've always used the shorthand, "m/s", I never saw that forward slash symbol as a division symbol; I never saw "m/s" as a fraction. I just saw it as a short way of writing "metres per second". I'm now wondering if this sounds absurd, that I've not seen it in this way. But, until now, it's not been put to me that it's a fraction.

So, why does, "m/s" mean, "metres DIVIDED BY seconds"?

If I walk at a pace of 2m/s, I cover a distance of 2m for every second that ticks by. Does that mean 2 metres DIVIDED BY 1 second? Which equals 2m (per second).

And if I walked at a pace of 2m/2s, i.e, 2m for every 2s that tick by, the fraction would be; 2m DIVIDED BY 2S, which equals 1m per second?

Apologies in advance if this sounds ridiculously basic.

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Prioritise. Persevere. No pain, no gain.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,422

Re: BBC Bitesize (Acceleration)

Hi paulb203,

.

.

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 240

Re: BBC Bitesize (Acceleration)

If I walk at a pace of 2m/s, I cover a distance of 2m for every second that ticks by. Does that mean 2 metres DIVIDED BY 1 second? Which equals 2m (per second).

And if I walked at a pace of 2m/2s, i.e, 2m for every 2s that tick by, the fraction would be; 2m DIVIDED BY 2S, which equals 1m per second?

Apologies in advance if this sounds ridiculously basic.

Your remark is good.

And you are right. In the expression (2 m/s), the forward slash symbol, in itself, doesn't represent a division as in the formula v=x/t.
In 2 m/s, it simply tells us that the result 2 came from a division (as mentioned by Jai).
Similarly, 2 m/s² just tells us that 2 is the result of two divisions.

---

Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

Oculus8596

Banned

From: Great Lakes,Illinois

Registered: 2024-09-18

Posts: 126

Re: BBC Bitesize (Acceleration)

When referring to speed on this page they often say things like,

“The bus has a constant speed of 10ms-¹"

I've not seen this before. I'm used to seeing speed given as simply, for example, 10m/s

Why the -¹ ?

I've noticed also for acceleration instead of saying, 10m/s/s, or 10m/s², they write 10m s -². Why might they do this?

I have never seen that before.

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The best things in life are not always free.

paulb203

Member

Registered: 2023-02-24

Posts: 317

Re: BBC Bitesize (Acceleration)

Thanks, everyone.
I'm going to let all of this brew for a while then come back to it

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Prioritise. Persevere. No pain, no gain.