How to describe This as an expression?

Hi

I have an Object which is moved by the Wind, in a special kind of way ( described below ).

( decimal values and pixels are allowed )

...

- **WindPower**, is a constant value

Every second:

- **WindVelocity** is increased by WindPower

- Object is **moved** 'WindVelocity number of pixels'

How do i describe the **Objects movement in pixels** as an expression?

Im not entirely sure, but i think this is close:

( ( T * ( T + 1 ) * ( T + 2 ) ) / 6 ) * WindPower

( Im sorry about the Title, but i dont know how to descibe it in a better way )

Re: How to describe This as an expression?

If v is the initial velocity (which is increased after the first step), then in t steps the object moves v + (v + p) + (v + 2p) + ... + (v + (t - 1)p) pixels. This is the sum of an arithmetic progression, and it equals (t/2)(2v + (t-1)p). If the initial velocity is increased before the first step, then the number is (v + p) + (v + 2p) + ... + (v + tp) = (t/2)(2v + + (t+1)p).

Re: How to describe This as an expression?

Hmmm

...

**EXAMPLE ( all values are potential floats )**

T = Time/ Seconds

WP = 0.5

Every second ( in this exact order ):

- Object moves WV number of pixels

- WV increases by WP

Expression defining Objects movement???

**SIMULATION**

T = 0

Object Move Total = 0

WV = 0

T = 1

Object Move Total = 0

WV = 0.5

T = 2

Object Move Total = 0.5

WV = 1

T = 3

Object Move Total = 1.5

WV = 1.5 ( Objcts total movement after 3 seconds )

**SOLUTION A**

( ( T * ( T + 1 ) * ( T + 2 ) ) / 6 ) * 0.5

( ( 3 * ( 3 + 1 ) * ( 3 + 2 ) ) / 6 ) * 0.5

( ( 3 * 4 * 5 ) / 6 ) * 0.5

( 60 / 6 ) * 0.5

10 * 0.5

Total Movement after 3 Seconds = __5__

No, that expression doesnt seem to be correct...

**SOLUTION B**

(t/2)(2v + (t-1)p)

What is 'p' supposed to represent here?

Initial Velocity of the Object, for the purpose of this expression, is 0.

The expression is solely suppose to reflect how Wind moves the Object, based on Time i guess.

Re: How to describe This as an expression?

**SOLUTION B**

(t/2)(2v + (t-1)p)

Sweet, this seems to work :D

There is no Initial Velocity ( 0 ), so its written simpler like this:

(t/2)(t-1)p

**PROOF**

( p = WindPower )

p = 0.5

(t/2)(t-1)p

( 3 / 2 ) * ( 3 - 1 ) *0,5

1.5 * 2 *0,5

1.5

...

Thanks again Emakarov!