'Out Of Gas'
Off-topic discussion. Wanna talk about corsets, duct tape, or physics? This is the place. Detailed discussion of any current-season TV must be whitefonted.
It takes 2 seconds to accelerate to 40m/s. 40m/s = 10 * t^2.
Well, fuck a duck.
From that you can figure the distance where d = vt + 1/2at^2
I don't remember anything.
Also, how does one correctly punctuate the first sentence?
You don't need that first comma.
All the whole "frictionless roller coaster" thing means is that the velocity can change direction without losing energy. And we can subtract the 1ms starting velocity from the ending velocity. So really, it's "how far does the roller coaster travel if it fell straight down, accelerated at 10m/s² and had a final velocity of 40m/s."
If the thingie traveled at a constant 40m/s for four seconds, it went 40m. But of course it was accelerating, so the distance would be less than that. Here's the trick: Because the acceleration is constant (eta: and the velocity started at 0), we can just divide the 40 in half.
d = vt
That's if your velocity is a constant. When there's an acceleration, you can't multiply those two things when v is different for each t!
So it's actually:
y=y0+v0t+0.5*a*t^2
(which is exactly your integral, because the integral over v, which is v=v0+at is exactly what I wrote above.)
[Edit: x-post integrals]
You don't need that first comma.
That's so not the big problem with the sentence.
If the thingie traveled at a constant 40m/s for four seconds, it went 40m
Not really paying attention to the problem as a whole--but in it is there a reason travelling 40m/s for 4s doesn't take you 160m?
If the thingie traveled at a constant 40m/s for four seconds, it went 40m.
So it WAS 4 seconds! v = at, not at^2. At least that makes sense.
y=y0+v0t+0.5*a*t^2
Where did the 0.5 come from?
What's the chances of her daughter not being totally screwed up?
Frankly, despite custody battles I think better than if ANS were still alive. I just hope there's an affectionate aunt or nanny in there to counterbalance the Daddy's Little Trust Fund effect.
Not really paying attention to the problem as a whole--but in it is there a reason travelling 40m/s for 4s doesn't take you 160m?
You're right.
But somehow I got the right answer. I sorta did it graphically in my head. Now I'm trying to figure out how to explain what I did....
Where did the 0.5 come from?
The integral of the velocity.
Where did the 0.5 come from?
When you do an integral of x^n, it is equal to a constant plus (1/(n+1))*x^(n+1).
[Take this and try to find its derivative - the opposite action to integral - and it's x^n]
So if we have v, the result of the integral is (1/(1+1))*x^(1+1)=0.5*x^2.
Look at all of you with your lovely math brains.
admires without understanding