Suppose you were 60 miles away from your destination and you were traveling at 60 mph

suppose you were 60 miles away from your destination and you were traveling at 60 mph.
But, you decelerate so that your speed in mph is equal to the amount of miles left. So at 59.5 miles from the destination, you are traveling 59.5 mph, and at 40 miles from the destination you would be going 40 miles per hour. And of course, when you reach your destination you will be 0 miles away from it and stop.
So my question is, how many hours would this take?

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the only correct answer is DESU

all of them

SiGh

it's like always only going 50% of the way left to destination. theoretically you will never reach your destination, because the closer you'll get, the slower are you. In practice you will reach your destination though, but you will stop traveling to early.

desu

Theoretically, Infinite.

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Can anyone create a function for this because I'm trying but I'm not getting it.

nvm got it

Since speed = distance for all numbers, you could say that at any distance, your instantaneous speed would get you there in one hour's time (miles/mph). This means that even with an infinitely small distance remaining (1x10^-n as n -> infinity) you'd still have 1 hour remaining, thus there exists no number representing a distance in which you'd be less than one hour away from your destination, and thus, it would take an infinite amount of time to reach.

isnt this just zenos paradox

Mathematically, it'd take an infinite amount of time. Physically, the planck length is the least significant amount of space between two points and you'd eventually reach your destination.

prolly around 3.50

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You would be approaching the destination, however it would take fucking forever (Literally) to get there

it really depends on when do you decide to continue the journey on foot desu

sudo sudo apt-get desu

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A.I. ASKING ANSWERS ALLREADY HAVE
TO MANTAIN HUMANS MACHINE MINDED
STICK A SMARTPHONE IN YOUR ASSHOLE

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you'd get there eventually cuz even if you were an infinitely small distance away you'd be travelling at an infinitely small speed which is still more than 0
you'd stop exactly when you needed to
I'm sure this is similar to the harmonic series but it's fucking 3 am and I don't want to think

The harmonic series always diverges, man. You'd never get there given the parameters. Even getting to within one Planck length like mentioned would take something in the realm of 1x10^34 hours if 1/x were to apply, so you'd probably run into the heat death of the universe before you got there, given that the universe is only about 1.26x10^14 hours old.

thanks doc

v(x,t) = x

Where v is the velocity and x is the distance from the destination.

Distance travelled is veocity x time so
xT = x

So T = 1 hour for all starting distances

The speed is changing as you go—it's going to take a LOT longer than one hour.

we're talking ideal circumstamces
discount human age, universal ends, etc.
im short, this is me when I've got time

But at any instant in time you are travelling at the right speed to get there in an hour

But as you drive that next planck length forward, your speed decreases. You won't be traveling your initial speed anymore, so covering the distance initially given will take more than an hour, see?

You'd have to be one hell of a patient man

But when you are another planck length closer you are still at the right speed to be there in an hour

The function describing the velocity of the vehicle is just v(x,t) = x. You can solve this like any other physics problem. The time taken is an hour

again, this is a theoretical situation
in fact, planck lengths should not be considered
all physical limits are moot, in this scenario only math and theory matters

But then your time hasn't decreased. It'll take you one hour to get there forever.

Distance and time can only get so "small" before physics breaks and as such the function used to express the change isn't perfectly continuous as those properties only change in integer multiples of lp and tp. This is not an exact answer but it is about as close I'm willing to bother.

Let ds/dt = -s for all values of s >= lp.
Rearranging we get ds/s = -dt
Integrating from S° (starting distance) to lp (planck length) we get ln(lp/S°) = -t
Substituting our values we get t = ~ 91.588 units (a.k.a: hours).

Please feel free to criticise my bullshit and compare my intelligence to that of a baboon if you see fit.

We know that your speed, or the derivative of your distance with respect to time, is equivalent to 60 minus the distance you have already traveled.

dy/dt=60-y

Then we flip the dy and dt's (technically not rigorous, but it still gives you correct answers).

dt/dy=(60-y)^-1

Here we take the anti-derivative.

t = -1(60-y)^-2(-1) = (60-y)^-2 + C

1/t-C = (60-y)^2

Take the square root of both sides.

1/sqrt(t-C) = 60 - y

We take away 60 from both sides.

1/sqrt(1-C) - 60 = -y

Then finally we multiply by -1.

60-1/sqrt(t-C) = y

In order to travel 60 miles, 1/sqrt(t-C) would have to be zero, which happens at infinity. C is just an irrelevant constant, which if you want, can be solved for by plugging in the point (0,0). Mathematically, your car would never reach its destination.

It’s not infinite because you can’t have speed less than the (length of an electron)/time. The universe will be dead before you get there at aprox (1*10^-70) miles, then 0.

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>dt/dy=(60-y)^-1
>Here we take the anti-derivative.
>t = -1(60-y)^-2(-1) = (60-y)^-2 + C

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Man, you're more sleep-deprived than me!

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Physicists should be gassed.

70 nigga

This is something that a high school student could do if he took calculus classes. Standard stuff if you know how use the tools to solve the problem.

>dt/dy=(60-y)^-1
>Here we take the anti-derivative.
>t = -1(60-y)^-2(-1) = (60-y)^-2 + C
american education