Velocity with air resistance help

In summary, we have a problem where the velocity (V) needs to be found using the equations V=Vo+AT and A=G-KV. The equation V=Vo+(G-KV)T is given, but it cannot be simplified because there is still a V in the equation. Phoenix suggests using the procedure of "replacement by an equal expression" to solve this problem. By using multiplication and distributive properties, and then factoring, we arrive at the equation V=(TG+Vo)/(1+TK). However, this equation is not applicable in this problem because the given equations are for constant acceleration, while the problem has changing acceleration.
  • #1
PHK
18
0
I need to find the velocity with the following information. V=Vo+AT and A=G-KV

so how would i find what V equals from this: V=Vo+(G-KV)T
 
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  • #2
Thats right. Is there something else to the question too? What velocity do you have to find?
 
  • #3
theres nothing else to the problem. i plugged in G-KV in for A in the first equation but now i have V=Vo+(G-KV)T. and i want to find velocity, but can't because there is velocity in the equation. so i want to know how to simplify the equation so i get V only on one side.
 
  • #4
did anyone figure it out yet?
 
  • #5
PHK said:
did anyone figure it out yet?

V=Vo+(G-KV)T

V = Vo + GT - KVT

V + KVT = Vo + GT

etc...
 
  • #6
I think this is right:

V=Vo+(G-KV)T = Vo+TG-TKV
V-Vo=TG-TKV
V-Vo+TKV=TG
V+TKV=TG+Vo
V(1+TK)=TG+Vo

V=(TG+Vo)/(1+TK)[EDIT]oops, looks like learningphysics beat me to it.
 
  • #7
"Replacement by an equal expression" is a procedure that is used a lot.
( like you replaced the "A" by "G-kV" )
"Multiplication, Distributive" ( Phoenix line 1 ) and
its inverse , "Factoring" (Phoenix line 5) are the basis of proportion.
When you add the negative of some term to both sides
(so that term cancels the original term on that side)
and/or divide both sides by the same factor
(so as to "move the factor to the other side")
... there's always more than one path that you can take
notice how Phoenix "undid" in line 4 , what he had done in line 2 ...
it is okay to take more steps, so long as you keep the goal in mind.
 
  • #8
thanks the equation works. i got one question tho. how did you get from this V+TKV=TG+Vo
to this V(1+TK)=TG+Vo?
 
  • #9
PHK said:
I need to find the velocity with the following information. V=Vo+AT and A=G-KV

so how would i find what V equals from this: V=Vo+(G-KV)T
Where did you get the equation V = Vo + AT? This equation is derived from calculus for the special case of constant acceleration. In your case, the acceleration is changing with speed, and is therefore not constant.
 
  • #10
PHK said:
thanks the equation works. i got one question tho. how did you get from this V+TKV=TG+Vo
to this V(1+TK)=TG+Vo?

he factored out the V... try multiplying out: V(1+TK)... what do you get?
 

1. What is the formula for calculating velocity with air resistance?

The formula for calculating velocity with air resistance is v = sqrt(2mg/cd). Where v is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, c is the coefficient of drag, and d is the density of the fluid.

2. How does air resistance affect the velocity of an object?

Air resistance, also known as drag, acts in the opposite direction of the motion of an object and increases as the object's velocity increases. This ultimately causes the object's velocity to decrease until it reaches a terminal velocity where the drag force is equal to the force of gravity.

3. Why is air resistance important in calculating velocity?

Air resistance plays a crucial role in determining the velocity of an object because it can significantly affect the motion of an object in the real world. Without taking air resistance into account, calculations of velocity would not accurately represent the actual motion of an object.

4. How does the shape of an object affect its velocity with air resistance?

The shape of an object can greatly impact its velocity with air resistance. Objects with a more streamlined shape, such as a bullet, experience less air resistance and therefore have a higher terminal velocity compared to objects with a larger surface area, such as a parachute.

5. How can velocity with air resistance be applied in real-world scenarios?

Velocity with air resistance is important in many real-world scenarios, such as designing vehicles and aircraft, understanding the motion of projectiles, and predicting the behavior of objects in fluid environments. It is also crucial in sports, such as cycling and skiing, where air resistance can significantly impact an athlete's speed and performance.

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