relation of variables t to a

[miringains]

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hey all, I always end up confusing myself on certain things such as the following

If a is reduced to a/6, what happens to t?

Originally I wrote down

x=1/2 at^2, rearranged for t and got t = sqrt(2x/a). Looking at this I thought alright, so it will increase by a factor of sqrt 6

But then I wrote down

Vf = Vo + at

And saw that they were just simply inverse of each other which means that t would increase by a factor of 6.


What is the problem in my thought process here?

 

[shaboobly]

hey all, I always end up confusing myself on certain things such as the following

If a is reduced to a/6, what happens to t?

Originally I wrote down

x=1/2 at^2, rearranged for t and got t = sqrt(2x/a). Looking at this I thought alright, so it will increase by a factor of sqrt 6

But then I wrote down

Vf = Vo + at

And saw that they were just simply inverse of each other which means that t would increase by a factor of 6.


What is the problem in my thought process here?

t= sqrt(2x/(1/6)a) = sqrt(12x/a); t increases by a factor of sqrt12.

wait im confusing myself.. i think your right about the 6 cause the 2 is already in it. idk about this example as i dont think time really depends on anything. maybe you gotta substitute one in the other to really figure it out, but i cant tell you for sure cause idk for sure. i have never seen a question asking time dependence on a.

something like F=kq/r^2; if r increases by a factor of 6, then f is decreased by a factor of 36 makes more sense.

 

[miringains]

forgot to mention that the correct answer is that it increases by a factor of 6

 

[shaboobly]

forgot to mention that the correct answer is that it increases by a factor of 6

in the second equation you can get t increasing by a factor of 6, but idk about the first one how to get 6. questions like these are stupid.

in the first eq you can get t^2 increases by a factor of 6, which is why this question is dumb.

 

[sciencebooks]

hey all, I always end up confusing myself on certain things such as the following

If a is reduced to a/6, what happens to t?

Originally I wrote down

x=1/2 at^2, rearranged for t and got t = sqrt(2x/a). Looking at this I thought alright, so it will increase by a factor of sqrt 6

But then I wrote down

Vf = Vo + at

And saw that they were just simply inverse of each other which means that t would increase by a factor of 6.


What is the problem in my thought process here?

I did this really fast in my head on intuition but I'm not sure that's the best way now that I'm seeing your equations. Anyway, I was basically thinking a=v/t so a is inversely proportional to t. Acceleration decreases, time increases.

 

[shaboobly]

I did this really fast in my head on intuition but I'm not sure that's the best way now that I'm seeing your equations. Anyway, I was basically thinking a=v/t so a is inversely proportional to t. Acceleration decreases, time increases.

way to simplify it 🙂.. haha i been doing too much review today.

 

[V5RED]

I did this really fast in my head on intuition but I'm not sure that's the best way now that I'm seeing your equations. Anyway, I was basically thinking a=v/t so a is inversely proportional to t. Acceleration decreases, time increases.

Assuming it is a projectile that OP is talking about that lands at the same height from which it falls, t=2v/a, but that gets the same answer as you got in terms of how much t increases.

y=vt-1/2gt^2
y=0 (because the displacement is zero once it lands)
vt=1/2gt^2
v=1/2gt (divided both sides by t)
2v/g=t (rearranged to solve for t)

 

[shaboobly]

Assuming it is a projectile that OP is talking about that lands at the same height from which it falls, t=2v/a, but that gets the same answer as you got in terms of how much t increases.

y=vt-1/2gt^2
y=0 (because the displacement is zero once it lands)
vt=1/2gt^2
v=1/2gt (divided both sides by t)
2v/g=t (rearranged to solve for t)

nice.. i love algebra. 2 more classes for a math minor 😎

 

[sciencebooks]

Assuming it is a projectile that OP is talking about that lands at the same height from which it falls, t=2v/a, but that gets the same answer as you got in terms of how much t increases.

y=vt-1/2gt^2
y=0 (because the displacement is zero once it lands)
vt=1/2gt^2
v=1/2gt (divided both sides by t)
2v/g=t (rearranged to solve for t)

👍

 

[miringains]

aaah that makes so much sense