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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

Today my book asked for the average velocity of a function AND the average speed of a function. Huh? I thought velocity and speed were the same thing and would have bet my life on it!

Somebody please explain this madness.

A logarithm is just a misspelled algorithm.

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

http://en.wikipedia.org/wiki/Velocity

and

http://en.wikipedia.org/wiki/speed

Havn't really had any of this yet, but you might find the answers there..

As far as I understand, velocity is a vector and speed is not..

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

OOoooh... I think I got it. speed = |velocity|

A logarithm is just a misspelled algorithm.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Yep, that's precisely it. With velocity, direction is important, but with speed it is not.

If you ran around in circles, your speed would be constant, but your velocity would be constantly changing. Your average velocity would be zero!

Why did the vector cross the road?

It wanted to be normal.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

If you ran around in circles, your speed would be constant, but your velocity would be constantly changing. Your average velocity would be zero!

And so would your IQ.

Take that, track team.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

here here, ricky!

A logarithm is just a misspelled algorithm.

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**Monox D. I-Fly****Member**- Registered: 2015-12-02
- Posts: 798

mikau wrote:

OOoooh... I think I got it. speed = |velocity|

Wait... Does it imply that speed can be negative? O.o

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Velocity can be 'negative' (although negative is not well-defined for vectors).

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**Monox D. I-Fly****Member**- Registered: 2015-12-02
- Posts: 798

How? Never encountered any.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,054

There is a formula for motion under a constant acceleration:

v = u + at

v is the final velocity; u the initial velocity; a the acceleration and t the time taken.

If an object is thrown upwards the student has to decide if 'up' is the positive direction for velocity, in which case the acceleration is negative. Both are vector quantities. Or you can take acceleration as positive, which makes v negative. It is not usual to consider time as negative, but it is a scalar anyway. I have encountered problems where the solution was a negative t, meaning an event happened before the start time.

Bob

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