Quick question concerning acceleration and distance...

[verso]

So first let me say that math is not my strong suit, and I'm not entirely sure that this is even a calculus question. I've never taken calculus before, and algebra is as far as I've gotten. So I'll just go ahead and apologize in advance.

This question, however, is a "real world" problem and one I'm very much curious about. The long and short of it is this...

I know that my car accelerates from 0-60 mph in 7.1 seconds. I know that my car traveled 30 feet. How fast could my car have traveled that 30 feet? In other words, I was stopped at a red light traveling 0 mph. The light turned green and I traveled 30 feet before being hit by an oncoming car. I need to know how long or how fast my car could have spanned that distance.

Is this an answerable question, or no? Thanks in advance!

 

[stapel]

So first let me say that math is not my strong suit, and I'm not entirely sure that this is even a calculus question. I've never taken calculus before, and algebra is as far as I've gotten. So I'll just go ahead and apologize in advance.

This question, however, is a "real world" problem and one I'm very much curious about. The long and short of it is this...

I know that my car accelerates from 0-60 mph in 7.1 seconds. I know that my car traveled 30 feet. How fast could my car have traveled that 30 feet? In other words, I was stopped at a red light traveling 0 mph. The light turned green and I traveled 30 feet before being hit by an oncoming car. I need to know how long or how fast my car could have spanned that distance.

Is this an answerable question, or no? Thanks in advance!

No, we cannot help you get out of whatever traffic ticket or citation you received (if that's what's going on -- which has always been my experience), at least not from only the information provided. You'll need to hire a qualified accident-reconstructionist or similar such professional in order to do this.

However, if you're interested in just bare-bones physics, then please provide the rest of the necessary information, starting with such things as: the road condition, the weather (including humidity levels), your tire wear, the weight of your vehicle (including the weights of the persons inside the vehicle at the time), and the specifics of your vehicle's acceleration pattern (especially noting the acceleration for each gear's range). Note: The "zero to sixty" acceleration time assumes "pedal to the metal". Are you stipulating that, as soon as the light turned green, you "floored it"?

When you reply, please include a clear listing of your thoughts and efforts so far, so we can see what model you're using and where you're getting bogged down in the computations. Thank you!

 

[verso]

No, we cannot help you get out of whatever traffic ticket or citation you received (if that's what's going on -- which has always been my experience), at least not from only the information provided.

I wasn't given a ticket, and I wouldn't need help getting out of a ticket if that had been the case. Math may not be my strong suit, but law very much is.

If you're interested in the back story and not the math, then I would be more than happy to relate my tale of vehicular curiosities, but it's really neither here nor there. If the question is unanswerable, then that's fine, but the assumptions I can do without -- however good-natured and well-meaning they may be. Thanks anyway.

 

[stapel]

I wasn't given a ticket....

There's a first time for everything. Glad to hear that I was wrong! :cool:

If the question is unanswerable, then that's fine....

It's not unanswerable, but it needs way more information. That's why the accident-reconstructionists cost so much (and why cops are given pre-installed software for when they do accident reports)! :razz:

 

[HallsofIvy]

So first let me say that math is not my strong suit, and I'm not entirely sure that this is even a calculus question. I've never taken calculus before, and algebra is as far as I've gotten. So I'll just go ahead and apologize in advance.

This question, however, is a "real world" problem and one I'm very much curious about. The long and short of it is this...

I know that my car accelerates from 0-60 mph in 7.1 seconds. I know that my car traveled 30 feet. How fast could my car have traveled that 30 feet? In other words, I was stopped at a red light traveling 0 mph. The light turned green and I traveled 30 feet before being hit by an oncoming car. I need to know how long or how fast my car could have spanned that distance.

Is this an answerable question, or no? Thanks in advance!

With constant acceleration, a, starting with initial velocity 0 and taking d= 0 as your starting point, your speed, at time t, is at and the distance you went is \(\displaystyle at^2/2\). Accelerating "from 0-60 mph in 7.1 seconds", a= 60 mph/ 7.1 seconds= 12.4 feet per second per second. So the distance traveled in t second will be \(\displaystyle 6.2t^2\) feet. Setting that equal to 30 feet, \(\displaystyle 6.2t^2= 30\), \(\displaystyle t^2= 30/6.2= 4.84\), \(\displaystyle t= \sqrt{4.84}= 2.2\) seconds and your car will have reached a top speed of (12.4)(2.2)= 27.28 feet per second= 18.6 mph.

 

[Deleted member 4993]

So first let me say that math is not my strong suit, and I'm not entirely sure that this is even a calculus question. I've never taken calculus before, and algebra is as far as I've gotten. So I'll just go ahead and apologize in advance.

This question, however, is a "real world" problem and one I'm very much curious about. The long and short of it is this...

I know that my car accelerates from 0-60 mph in 7.1 seconds. I know that my car traveled 30 feet. How fast could my car have traveled that 30 feet? In other words, I was stopped at a red light traveling 0 mph. The light turned green and I traveled 30 feet before being hit by an oncoming car. I need to know how long or how fast my car could have spanned that distance.

Is this an answerable question, or no? Thanks in advance!

No this is not a calculus question
Your initial velocity = 0 = u

Your acceleration = (60*5280/3600)/7.1 ft/s² = a

distance travelled = 30 ft. = S

assume

the velocity of your car at impact = v

the time elapsed at impact = t

assuming constant acceleration:

v² = u² + 2 * a * S ..... calculate v and then use

v = u + a * t .............. calculate t

Simple algebra and a bit of physics - will satisfy your need.

 

[stapel]

...assuming constant acceleration...

...which, of course, is very not true of a geared vehicle in acceleration from zero! :wink: :lol:

 

[Deleted member 4993]

...which, of course, is very not true of a geared vehicle in acceleration from zero! :wink: :lol:

What if - he had a jet-propelled car from "Jetsons" and got to the final (constant) acceleration in 10^-17 seconds!!!

 

[verso]

Thanks for the replies everyone, and I apologize if my second post there came off as being a wee bit snarky. I wasn't expecting any other replies. Anyway...

With constant acceleration, a, starting with initial velocity 0 and taking d= 0 as your starting point, your speed, at time t, is at and the distance you went is \(\displaystyle at^2/2\). Accelerating "from 0-60 mph in 7.1 seconds", a= 60 mph/ 7.1 seconds= 12.4 feet per second per second. So the distance traveled in t second will be \(\displaystyle 6.2t^2\) feet. Setting that equal to 30 feet, \(\displaystyle 6.2t^2= 30\), \(\displaystyle t^2= 30/6.2= 4.84\), \(\displaystyle t= \sqrt{4.84}= 2.2\) seconds and your car will have reached a top speed of (12.4)(2.2)= 27.28 feet per second= 18.6 mph.

It took me 3 hours of trying to figure it out all on my own, and this is actually what I came up with but I wasn't sure that it was right. And by "right," I mean a close-enough approximation. I know that we can factor in the tread on the tires, weather conditions, etc. but as someone here has already mentioned, actually reconstructing car accidents is someone else's job.

Thanks!