A Question of Speed

...as would be the acceleration and deceleration. The human body has not yet evolved to the point where it can withstand such things.

Can relativistic effects be ignored?

One cannot advocate the breaking of laws such as road speed limits.

What if the Cavalier were brand new and had 10 miles on the odometer ... it's a Cavalier - never mind.

If the Cavalier came equipped with a flux capacitor it could make the trip averaging 60 mph with no problem. :)

But what if it wouldn't start? Cavalier's are known to do that quite often.

I know of a Delorean that wouldn't start and it almost left someone many years in the past - he actually did get it started and the 1.21 Giga Watts from the lightning bolt which struck a clock tower at precisely at 10:04 PM on November 12, 1955 was transferred to the car via a hook device and the car ... it just ... vanished ...

FYI, the motor in the Delorean was a PRV 2.8L - the same motor used in the Volvo 260 series, though Volvo also used a 2.7L version in earlier 260's. We owned a 1979 265 Wagon with the PRV 2.7L. What a terrible motor! The little 2.1L was a much better choice, but that was a real Volvo design. The PRV was a joint effort by Peugeot, Renault and Volvo. https://www.youtube.com/watch?v=YZzGOglN7SE

One would put on a lot of weight by so doing.

GA!

Regrettably, even the speed of light is finite!

Yes, but at c it would take zero time to travel the distance, so it works (ignoring acceleration and deceleration)

What time would the guys on the road say it took? Would it be 30 miles/c?

"Would it be 30 miles/c?"

Yup, I guess one can put it that way - they will observe 1 hour and 30/186000 seconds. For all engineering purposes, it's just 1 hour.

Thanks. I was just referring to the 2nd 30 miles.

The question is, did she come home with something she didn't want???

Anyway, you made me laugh, which is a good thing in these days of Covid!

Not really correct, because at the earth frame of reference, the time it would take for a light beam to get from the halfway point to the destination is still greater than zero.

How can you be in two places at once, if you're not anywhere at all.

"How can you be in two places at once, if you're not anywhere at all."

I can't, but a photon can...

Einstein ignored them..he married his cousin...

Tardiness is to be eschewed.

Warp Factor 1 should do it.

"Ye cannae break the laws of Physics, Captain."

It's a shame there is no Good Question button.

Then he would have left an hour earlier...

To my surprise it is not necessarily an hour earlier. Our Australian members know about this.

Indians and North Koreans too.

Or, the trip could've occurred when we're going from daylight saving to regular time or vice versa - depending on the direction of travel.

I don't answer questions.

This is impossible.

To have an average speed of 60mph during 60miles you need to drive the total 60 miles in 1 hour. As you have already use 1 hour for the first 30 miles at 30mph, it is too late: you just have no time to drive the second part to finish the 60 miles in 1 hours.

Maybe when we better know about black hole system and the way to go through "universe" and envisage teleportation it could be achievable ...

As I read the question, it doesn't state a 1 hour limit. As a guess, I go for 90MPH for the last 30 miles. Please don't kill me if I misread the question.

Rod.

I'm afraid that 60 miles at an average speed of 60 mph does imply a 1 hour limit.

Sorry, fresh out of thyme!

With people proposing a velocity seven orders of magnitude greater than the given velocity with only a single significant figure and distances of only one significant figure the precision of all measurements are circumspect, even those given.

This is a trick question. You would need to be in the future and be "flying" a space ship that can travel the speed of light. Or you could use a time travel machine and visit Rome, Tokyo, Melbourne, Rio, London, Shanghai, Istanbul, Lima, Pretoria and New York City first, then travel backwards in time and arrive at the starting point at the exact time you arrived in town.

Solar, you are a trickster!

This is possible, but very unlikely. Follow this logic for a second.

The question states an average speed of 60 mph, not 60.0 mph. So with rounding, we need to go at minimum 59.5 mph - rounds up to 60.

Divide 120 miles by 59.5 mph and you get 2.01680666666 hours - 2 hours for the first 60 miles = 0.0168066666 hours. Divide 60 miles by 0.0168066666 hours and you get 3,570.26 mph or Mach 4.69 - call it 4.7. The X15 could do it and it was manned.

"The question states an average speed of 60 mph, not 60.0 mph. So with rounding, we need to go at minimum 59.5 mph - rounds up to 60."

Or one can be a "un-engineering-like" stickler for precision and say that even at 30 mph, the car's clock time dilated by ~1 part in 10¹⁵, so that you have arrived at the 30 mile road sign in 3.6 picoseconds (ps) less than 1 hour. So then you have 3.6 ps to do another 30 miles, giving you a required speed of less than c. But by how much less?

Anybody wants to take a shot, keeping relativity in mind...

Has anyone got any Aspirin, please?

"Or one can be a "un-engineering-like" stickler for precision and say that even at 30 mph, the car's clock time dilated by ~1 part in 10¹⁵, so that you have arrived at the 30 mile road sign in 3.6 picoseconds (ps) less than 1 hour. So then you have 3.6 ps to do another 30 miles, giving you a required speed of less than c. But by how much less?"

There are more than one way to skin this cat, but for me it is easiest via Lorentz contraction of the 30 miles. So the equation to be solved for speed v is:

Distance in the Lorentz contracted car frame: v t = d √[1-v²/c²]

Collecting the v-terms gives: v = d / t / √[1+(d/ct)²]

Due to the very small time that we work with, this requires 1 to be added to a very large number, (d/ct)² = 2E+15 and the sqrt taken. Unfortunately v is not straightforwardly computable in my Excel, because adding 1 to 2E+15 leaves it at 2E+15.

The value of the sqrt will change by the order 1 part in 2E+15. This should be how close to c the required speed would be, of the order 150 nm/sec less than the speed of light (unless I'm confused by the units here).

Anyway, a pretty useless exercise, but somewhat educational...

@Jorrie

You're overthinking this. The precision involved in finding an average speed is nowhere near 1/2E+15. Also, the accuracy in measuring out the exact distance was most likely on the order of within +- 1/10 mile accuracy, though the OP states it as +- 1 mile (no tenths in the question).

I think we should just chalk this up to a very high speed on the return trip, in the order of Mach 4 or 5. There's no car that can accomplish this, so the actual answer is "I can't be done with the technology we have today."

I think the OP intended it as a fun thought experiment, where impracticality is not a limitation. Clearly, the standard Newtonian answer is that you would need infinite speed to complete the trip in one hour. I have just shown that there is a relativistic answer as well.

One normally does not do the relativity stuff on speeds like 30 mph, but the type of calculation that I have shown does appear in real life space projects, where "relativistic tortoise and hare" situations do come up.

HiTekRedNek gave permission to end my contribution with this super-creation of his (for use on CR4 exclusively):

A photon,which is mass less,
Fell into a pool of molasses
He knew he was in trouble
When passed by a bubble
The bubble was entangled you see,
And it doesn't make sense to me
Nor to Professor, A.E.
(c) 2020 hitekrednek

He mentioned 60 mph, so we're rounding to the nearest whole number. If he said 60.0 mph, we'd round to the nearest 1/10th. Or 60.00 would be rounding to the nearest 100th.

I remember quite a few years ago where one should only round to the precision of the result. In the example from the OP, I don't think the distance was measured very accurately - 60 miles, not 60.0 or 60.00 miles. Time could be measured more accurately - we don't know.

Come to think of it, nothing in the original question said the 60 mile path was the shortest path. Maybe a short cut is only 30 miles.

Now you're thinking! Though would it be possible to drive 30 miles in a very small amount of time?

If you are an entangled particle,you could travel the remaining distance in no time...

Kinda spooky,eh?

No need to entangle, just make yourself massless...

As in a Catholic who decided no more church???

But could you drive the distance in no time???

What about if it was a round trip?...and you had to stop for gas, which took 10 minutes...

Add Alcubierre Warp Drive to car

I don't trust that, I might get trapped in inner space...

Is this <...60 miles...> measured along a Great Circle at one altitude between those two places and can one travel via a straight line instead with a varying altitude?

That sort of straightened route will save you ~36 inches town-to-town, so it may save you from having to go at c for the the second half of Solar's route. But a pitstop? Nah...

“Are we there yet?” - from the back seat.

The thread says <...drive...>, so it’s a road motor vehicle with a steering wheel based on that verb. Very few road motors are <...36 inches...> long, so the distance has a lack of precision by at least this amount. Then the road might not be straight by that amount or at constant altitude by that amount. Does this vehicle follow a Great Circle or does it track slightly from side to side so as to pass safely slower vehicles...

Oh, dammit - more Aspirin, please.

This of course begs the question: if you were to take that route in a cavalier (ie. rolling), ignoring friction and wind resistance how long would it take?

It depends on how hard one is pushing it, which in turn depends on whether the rear screen heater is working well enough to keep the hands warm.

At least one isn’t trying it in a cast iron bath. Much higher drag coefficient...

"This of course begs the question: if you were to take that route in a cavalier (ie. rolling), ignoring friction and wind resistance how long would it take?"

The more "engineer-relevant" question would perhaps be: what is better - build that 'straight' road above or below the surface of earth - i.e. dig it or pylon it?

Tip: Newton's shell theorem

It turns out that the answer to the ultimate question is "forty two" minutes

The above linked video explains how to calculate it. Surprisingly it's independent of the two points chosen: ie the same for a fall through the centre of the earth or a slide from London to New York or a slide from town A to town B 60 miles away.

It is even independent of the size of the planet. The only variable in the equation is the density of the planet.

Randall, that's a trick question. The last time I saw a Cavalier on the road was ... ummm ... well, it's been a while. So there are 0 Cavaliers still running (we haven't had a Cavalier questions for a while here, so they have to be all dead), therefore, a Cavalier wouldn't be on the road, so the answer is infinity. It would take forever to get a Cavalier anywhere, since they're all in the junk yard.

The man's journey thus far has taken him to the edge of a mountain ridge, the town of destination is below in the valley, the path down is a 30 mile long and winding road, the man parks his car and jumps off the cliff with a parachute, when he leaves the cliff he is immediately in the towns' airspace....

How fast does he need to fly to average Mach 5 (reference to Speed Racer)? And what happens if he accidentally sees a Cavalier driving through town? Again, we haven't had any Cavalier questions in a while, so he must be hallucinating.

I remember seeing a Cavalier on the road once,err..beside the road.

It sat there for months because it ran out of gas.

The value of a Cavalier is more than doubled if it has a tank full of gas.

Empty gas tank= no value.

If you find a Cavalier with an empty gas tank,it was siphoned out.

They will not run long enough to use a full tank of gas...

That was funny! I got a good laugh - Thank you!

As I've been driving across five states, I've noticed that Cavalier's are no longer on the side of the road broken down. The new champion is the Dodge/Plymouth Neon - Plymouth/Chrysler PT Cruiser. We've seen quite a few on the side of the road and very few running.

If any reader has some form of missile that can be thrown at SolarEagle at <...30mph...> causing pain on arrival and impact, will that reader please make it known?