Finding final 'X Velocity'

Hi

I have never been very good with advanced math, and i dont even know if this is the correct area to ask this kind of question.

But anyway here goes:

...

I have a Ball and i want to determine its final X Velocity after X seconds

Lets say the Ball has no initial X Velocity and starts at coordiantes 0,0.

Lets say the Balls X Acceleration ( Wind Acceleration ) is increased by 1 every second.

Lets say the totall flight time of the Ball is 6 seconds ( this is variable ):

**BALLS X ACCELERATION** ( for each second )

1, 2, 3, 4, 5, 6

**BALLS X VELOCITY **( for each second )

1, 3, 6, 10, 15, __21__

...

The data i am interested in retrieving is the Balls final X Velocity __21__, but i want a formula wich automatically determines this **final X Velocity based on X Acceleration ( in this case, 1 ) and Flight Time ( in this case, 6 Frames )**.

I have tried for a long time to figure this out but have not make any headway yet.

*Any* help as to how i can find Final X Velocity would be much appreciated :)

Thanks

Re: Finding final 'X Velocity'

your table values for velocity are incorrect based on the way you have defined acceleration ...

for $\displaystyle t$ in seconds ...

$\displaystyle a = t$

$\displaystyle v = v_0 + \frac{t^2}{2}$ , where $\displaystyle v_0$ is the velocity at time $\displaystyle t = 0$

Re: Finding final 'X Velocity'

Thanks for the reply Skeeter!

Although i fail to see how that simple formula can yield the number 21 in the above example

Asi said, ive never been particularly good at this stuff.

I might be using the wrong terms or something, but regardless the data i have listed above is correct.

...

Let me clarefy.

This is what happens every second in the exact order:

- Wind Power is increased by 1 ( meters per second )

- Wind Power is *added* to the Balls X Velocity ( meters moved per second )

- Balls position is moved 'X Velocity' number of meters to the right

After X number of seconds, i want to know what the X Velocity of the Ball is.

...

As i already said i might be using wrong terms or words, so feel free to correct me so i wont make the mistake in the future.

Re: Finding final 'X Velocity'

Quote:

Originally Posted by

**CakeSpear** **Although i fail to see how that simple formula can yield the number 21 in the above example**

as I said ... your given acceleration will not yield the values you have for velocity

Asi said, ive never been particularly good at this stuff.

I might be using the wrong terms or something, but regardless the data i have listed above is correct.

...

Let me clarefy.

This is what happens every second in the exact order:

- Wind Power is increased by 1 ( meters per second )

- Wind Power is *added* to the Balls X Velocity ( meters moved per second )

- Balls position is moved 'X Velocity' number of meters to the right

After X number of seconds, i want to know what the X Velocity of the Ball is.

...

As i already said i might be using wrong terms or words, so feel free to correct me so i wont make the mistake in the future.

if you wish to have the velocity ...

v = 1, 3, 6, 10, 15, 21 for t = 1 , 2 , 3 , 4 , 5 , and 6

the velocity would be $\displaystyle v = \frac{t(t+1)}{2}$

and the acceleration would be $\displaystyle a = t + \frac{1}{2}$

Re: Finding final 'X Velocity'

Thanks again Skeeter!

That formula works mint for the example i gave!

I however forgot to mention that the Wind Power need to be variable ( any Decimal or Integer ).

Say if i change the Wind Power to 2 ( or any other number ) for example:

v = 2, 6, 12, 20, 30, 42

The above formula fails to produce correct results.

Thanks again :)

Re: Finding final 'X Velocity'

Quote:

Originally Posted by

**CakeSpear** Thanks again Skeeter!

That formula works mint for the example i gave!

I however forgot to mention that the Wind Power need to be variable ( any Decimal or Integer ).

Say if i change the Wind Power to 2 ( or any other number ) for example:

v = 2, 6, 12, 20, 30, 42

The above formula fails to produce correct results.

Thanks again :)

Understand that if you create a new function for velocity, its time rate of change (acceleration) also changes.

now, if you want v = 2, 6, 12, 20, 30, 42 (which is double your last velocity function)

$\displaystyle v = t^2 + t$

$\displaystyle a = 2t + 1$

note the acceleration also doubles.

Understand that acceleration is the derivative (time rate of change) of velocity ... there is no getting around that.

if you change velocity, you change the acceleration

Re: Finding final 'X Velocity'

Yes i understand that.

Logicaly if an Objects Acceleration changes, its Velocity will also change.

...

Let me tell you more about the background for this question:

I have somewhat of a computer programm wich launches a Ball of a Cliff at an Angle and Speed.

I am now trying to determine the Balls Final Xposition along Ground Level.

I have been following this video:

Projectile motion - YouTube

I see now that the way the video finds "Final Xposition along ground level" is:

Final X velocity * flightTime

Wich will not work for my situation since my Ball is affected by Winds and so Xvelocity is not constant.

Re: Finding final 'X Velocity'

Quote:

Originally Posted by

**CakeSpear** I see now that the way the video finds "Final Xposition along ground level" is:

Final X velocity * flightTime

Wich will not work for my situation since my Ball is affected by Winds and so Xvelocity is not constant.

In general, you can find the position function by integrating the velocity function with respect to time. If we use that last equation, $\displaystyle v=t^2+t,$ the position $\displaystyle s$ at time $\displaystyle t$ would be given by $\displaystyle s(t) = \frac13t^3+\frac12t^2+s_0,$ where $\displaystyle s_0$ is the initial position.

Re: Finding final 'X Velocity'

Reckoner, Ill have to take some time and try to diges what you just said.

Well in my programm i am already able to ( by help from the above video ) determine:

- The Balls Final Y velocity ( with decimal presicion ) as it hits ground.

- The Balls total flight time ( with decimal presicion ) before it hits ground.

Regardless of launch Angle or Speed, before the Ball even starts moving.

Can this help me in any way?