Momentum and Pressure and Forces

[Pawnag3]

This is a theoretical question that I have, it might be somewhat elementary, or I might be missing something. Basically, we have two formulas:
1) We know that
P = F/A
By multiplying by d/d, we get:
P = Work/Volume
P = Energy/Volume
P = 1/2 mv² / V
Therefore
F/A = 1/2 mv² / V
And therefore, the force is equal to the velocity squared.
2) However, according to F*t = mv
We say that Force is directly proportional to velocity.

Do you see the contradiction?
Please Help

Note: I'm basically comparing the relationship of force with respect to velocity

 

[The legend]

F/A = 1/2 mv² / V
And therefore, the force is equal to the velocity squared.
2) However, according to F*t = mv
We say that Force is directly proportional to velocity.

Do you see the contradiction?

in the first sentence
$$\frac{F}{A}=\frac{1}{2}\frac{mv^2}{V}$$
Now when you bring the area on the other side A/V becomes 1/length or 1/distance and cancels with one (length)² of velocity ... hence there is only one velocity term left and hence F proportional to v.

Another mistake is you have considered F*d=Work but actually its the dot product between them.

Rem: F/A is proportional to v² not force!

 

[Pawnag3]

Umm, thanks, that clarifies everything :D
But I have one question:
1) How did you make the formatting look so nice? :D
I couldn't figure it out (but then again, I didn't spend too much time, under which heading is it? :P)

 

[The legend]

Umm, thanks, that clarifies everything :D
But I have one question:
1) How did you make the formatting look so nice? :D
I couldn't figure it out (but then again, I didn't spend too much time, under which heading is it? :P)

I used latex or tex as its called ... you can learn it here
https://www.physicsforums.com/showthread.php?t=386951