I was on another thread argueing something stupid, but anyways I'm curious about something..

If a 350z does 1/4 in 14.1 secs @ 99.6 mph
and a Civic SI does the 1/4 in 15.7 secs @ 88.4 mph
(These are times I pulled of a drag racing site which had time slips)

and both cars were racing side by side, would not the car length between the two cars at the finish line be around 6.8 cars? Curious because another member said it would be around 15 car lengths... I figured average car length for both cars to be about 16 feet.


Just curious if anyone knew the equation for figuring it out...


Thanks

 

my kinematics must be screwed up, 'cause i was getting ridiculous answers...

anyways, just hand-jamming it... at the end of 14.1 seconds, the civic was moving at about 79mph, so in the last 1.6 seconds it was averaging 84mph...

84mph over 1.6 seconds = 197 feet which is about 12.5 car lengths...

 

Built using calculus I got 7.

 

Since both cars are moving you have to find the velocity of the two cars. Well the Tracks computer is using a function to compute times@mph based at 1/4. Since we dont know the function we use the two times given as points (time, mph).

You use y2-y1/x2-x1=-7 (negative in physics the way its traveling) This is the most acurrate because it takes in the account at the point for both cars at the 1/4 mile mark.

You can use that to compute the given distance at any time.

not sure if thats how you solve this problem?

 

hahaha this is interesting.

 

60foot will be better on the civic...

 

1.6 second difference between the 2 cars

trap speed of civic is 88.4mph.

simplest and quickest approximation is therefore.

1.6s * 88.4mph =207 feet
= 13 car lengths

this is an approximation though, to have correct answer you would need the average speed of the civic during the last 1.6 seconds. But since acceleration is NOT linear from start to finish, there is no precise way of knowing the speed of the civic at the time the 350z was crossing the line. Might as well use trap speed. A car like civic will not be accelerating much at end of 1/4mile.

 

That cant be right? Then one could say well the trap speed of the 350Z is 99.6mph and he is ahead 1.6 seconds. Since mph is more he will be ahead more.

Also you cant do it that way unless you used conversions (even then it would be wrong). Since 1.6 is in seconds the only way you could multiply them together would be if you changed 88.4 mph to Miles Per Seconds first. Now you want feet so you would have to change 88. 4 MPS to Feet Per Second.

Then it would be (1.6s*_____fps)/15ft

Again that cant be right?

 

like i said, last night my brain was hurting (probably the whisky) -- but stay away from numerous conversions if you could... using v^2 = vo^2 + 2as and s = Vo*t + .5at^2 i was getting really wild answers... like 50 car lengths...

i guess i'm saying, the more you drink the more interesting the calculations become

 

but as a caveat, the approximation is as close as you're going to get without an accelerometer, so i'm stickin' with 13 cl

 

dude dude

You need to think about the problem at hand first, not just randomly multiply numbers.

Why would you use the 350z speed to calculate how fast the civic covers the remaining distance? It's the civic speed that you must consider. The speed of the 350z has nothing to do with anything.

when the 350z is at the line, the civic is exactly 1.6 seconds behind at a speed very close to 88.4mph (as I said, it's an approximation).

You get the size of the "gap"(or distance to the finish line), by multiplying the speed of the civic by 1.6sec.

Obviously you need to convert mph in fts. 88.4mph = 129.65 fts. no big deal (just divide by 3600 and multiply by 5280).

129fts * 1.6s ~ 207ft
207/16 ~ 13 car lentghts

 

For the first car...

x=total distance the cars traveled = 1320 feet
x(initial) = 0
v(initial) = 0
t = time taken to run the 1/4 mile

x = x(initial) + [v(initial) * t1] + [1/2 * a * t1^2]

1320 ft= .5 * a * (14.1 sec)^2

a = 13.28 ft/sec^2

For the second car...

using the same equations

a = 10.71 ft/sec^2

Now, plugging in the time of 14.1 sec into the slow cars run and calculating the amount of distance he had to travel to catch up (or the distance he was lagging...)

x (fast car) - x (slow car) = 1/2 * a * t^2

where x (fast car) = length of the track = 1320 feet
a = 10.71 ft/sec^2 (from the slow car above)
t = time it takes for the fast car to finish the race = 14.1 sec

[1320 - x (slow car)] = 0.5 * (10.71 ft/sec^2) * (14.1 sec)^2

x (slow car) = 255 feet

Now take 255 feet and divide by the length of the 350z and VIOLA... (196.4 inches = 16.37 feet long)

The Z won by... 15.6 car lengths!

 

BINGO!!!!!!! we have a winner......... Neffster gets the cookie for today.


the quick and dirty approximation is close but the actual correct answer is ~15.6. (that is what i got as well)

neffster- ME or physics professor? i hated doing all that physics crap in college..... but i always was good at it and dynamics.

 

that is largely inacurate, as it assumes acceleration is constant.

which could not be farther from the truth

there is a HUGE difference in acceleration in the firt 200ft, compared to the last 200ft.

 

regardless... it's as close as you'll get without a continuous differential map... or a g-meter

 

exactly, the only way you can get a close answer is to assume acceleration is a constant.

 

wow, i haven't needed math since my freshman year of college, ouch, my head hurts now.
all you math guys have my utmost respect

 

I still don't agree.

a civic will be accelerating very slowly during the last 1.6 seconds. Very far from that 10.71 ft/s^2.

in the last couple of second it's speed varied max 1-2-3mph. The civic is starting to be maxed out, it's speed is almost constant.

If you use 10.71fts^2, you get that in the last 1.6 sec it's speed varied by 11mph, which is absolutely impossible for such a car.

answer is closer to 13 cars

 

jeebus...

i might as well go buy a g-meter and test this

gotcha, noted... all we're doing is using the best approximations you can reasonably assume without more data...

get those data and then you can be much more accurate in your calculations, until then....

oh well... the civic got whupped either way

 

now, if you had a speed map you'd be able to pull an approximation of the instantaneous accelerations throughout the quarter...

when you see those speed curves in mags, linear acceleration would look like a line w/ unchanging slope from 0mph to end of race... it's not exact, but it's moreso than picking some mph variation over the last 1.6 sec of the race out of thin air and calculating car lengths...

again, point is moot... another reason everyone should have a datalogger or g-meter