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**paulb203****Member**- Registered: 2023-02-24
- Posts: 278

I’m trying to apply Gauss’s formula for adding consecutive integers to the first second of a freefalling object.

The formula is n(n+1)/2

E.g, to add the numbers 1 to 100 we do,

n=100

100(100+1)/2

=100(101)/2

=10100/2

=5050

*

During the first second of freefall an object, I’m told, averages a velocity of 5m/s downwards (is this the average of Om/s and 5m/s?) *edit*; (is this the average of 0m/s and 10m/s, not the average of 0m/s and 5m/s)

I’m assuming that one way to get this average would be to divide that first second into tenths, add the ten corresponding velocities, and divide by 10.

So for the first tenth we would reach 1/10m/s, for the second tenth we would reach 2/10m/s, etc, up to the tenth tenth where we reach 10/10m/s.

Using Gauss’s formula for the addition we get;

n(n+1)/2

n=10

=10(10+1)/2

=10(11)/2

=110/2

=55

Which we divide by 10 as we’re talking about tenths, so we get 5.5

But the average velocity for the first second of freefall is 5m/s, not 5.5m/s.

Where am I going wrong

*Last edited by paulb203 (2024-09-24 22:11:31)*

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,583

From the (newtonian) equations of motion for a object falling from rest with an acceleration g (ok to take this as 10m/s/s) the final velocity is given by v = 0.5gt^2

So when t = 0.1 v = 0.05

t = 0.2 v = 0.2

t = 0.3 v = 0.45

................................................

t = 1 v = 5

The v values aren't in arithmetic progression so that formula won't work.

Bob

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**Oculus8596****Banned**- From: Great Lakes,Illinois
- Registered: 2024-09-18
- Posts: 126

Bob wrote:

From the (newtonian) equations of motion for a object falling from rest with an acceleration g (ok to take this as 10m/s/s) the final velocity is given by v = 0.5gt^2

So when t = 0.1 v = 0.05

t = 0.2 v = 0.2

t = 0.3 v = 0.45................................................

t = 1 v = 5

The v values aren't in arithmetic progression so that formula won't work.

Bob

Is this a physics problem? Objects falling implies physics.

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**paulb203****Member**- Registered: 2023-02-24
- Posts: 278

Bob wrote:

From the (newtonian) equations of motion for a object falling from rest with an acceleration g (ok to take this as 10m/s/s) the final velocity is given by v = 0.5gt^2

So when t = 0.1 v = 0.05

t = 0.2 v = 0.2

t = 0.3 v = 0.45................................................

t = 1 v = 5

The v values aren't in arithmetic progression so that formula won't work.

Bob

Thanks, Bob.

Are you sure of that equation?

I thought it was v=gt.

E.g, v=10x1

v=10m/s

I.e, an object in freefall reaches 10m/s after 1 second (with an average of 5m/s for the period 0-1s)

*

Your equation seems to give that average.

Forgive me if I'm wrong, my brain is starting to hurt after an hour on this

(Just got this from the Google AI overview; To find the final velocity of a free falling object, you can use the formula v = gt)

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