Stuck in a question from exam -- Car decelerating to avoid hitting an obstacle

[bob012345]

Then we will calculate the other unknown values in a normal way without the third stage of the addition of the two distances since Xo is 0. i think i understand those types of exercises now.

I think it would be easier to first compute the distance traveled before the driver could react which you did at 5m then simply say the obstacle is now 85 m away. Simply ask can the car going 33.33m/s stop in 85 m at an deceleration of -6m/s^2?

Using $v_f^2 - v_0^2 = 2 a \Delta {x}$ we have with $v_f = 0$ $\Delta {x} = \large \frac{-33.33^2}{2(-6) m/s^2} = 92.6m$ which is greater than the 85m left to go so it crashes.

You could also ask how fast is the car going when it crashes?

 

[Delta2]

Yes the exact time and speed at the moment of collision would be another nice question for this problem.

 

[PeroK]

Here's how I would have done this problem. First, I would have calculated the vehicle's stopping distance, based on the deceleration of $-6 \ m/s^2$ and the initial speed of $33.3 = \frac{100}{3} \ m/s$. As the final speed is $v = 0$ and using $v = u + at$ we have:
$$0 = \frac{100}{3} \ m/s + (-6 \ m/s^2)t$$ which gives
$$t = \frac{100}{18} = \frac{50}{9} \ s$$I would then use that the average speed for deceleration to rest is half the initial speed. So, $v_a = \frac{50}{3} \ m/s$. And the distance traveled is $$s = v_at = \frac{50}{3}\frac{50}{9} \ m = \frac{2500}{27} \ m \approx 92.6 \ m$$So, we can see that the vehicle needs more than $90m$ to stop, even without the reaction time.

Note that an alternative approach is to use $v^2 - u^2 = 2as$. And, with $v = 0$, $a = -6 \ m/s^2$ and $u = \frac{100}{3} \ m/s$ we have:
$$s = \frac{100^2}{9 \times 12} \ m = \frac{2500}{27} \ m \approx 92.6 \ m$$Which is the same as before.

Although we don't have to calculate the additional distance covered during the reaction time, we know that it is $5m$. That means the total stopping distance (reaction plus braking) is $97.6 \ m$.

Note that a better problem would have the obstacle $95 \ m$ ahead, as that would require us to calculate the reaction distance.

 

[bob012345]

i think i understand those types of exercises now.

That is our goal. Good luck on your exam!

 

[Nik_2213]

A tad rusty on the math, but I dredged my 'v=u+ft' and 's=ut+0.5ft^2', set to work.
First, convert that innocuous kph to m/s. I lived by mph & fps, but same implacable math applies.
Yup, at that speed, you lose a car's length before the 'Reed Alert' kicks in.
Assuming you brake then swear, you're still a limo 'long'.
You and your passengers are wearing seat-belts, yes ??

( Air-bags are good, but deflate just in time for next vehicle's impact to hurl you through screen... )

Which is why the careful driver must anticipate rather than simply react, while limiting speed to worst-case scenario...

( Eyes on stalks. Scan traffic flow for ijits: Remember, they're all out to get you... )

Funny story for you:
One of our truck drivers had a lapse on motorway, plowed 40-ton 'artic' into standing traffic. Wasn't 'speeding', on the phone or anything, just sort of blinked. So, all of us insured to drive on company business, with truck or car, had to do an urgent road-safety course. Finale was a poster-sized hazard-spotting 'toon. Think 'Hectic, Very Cluttered Side-street'. Ring all the horrors. Pass was 16/20.
There was much hilarity when I handed in my sheet with 24 'potentials' ringed.
Until our 'Health & Safety' boss took a closer look, decided mine were all valid, made a few calls.
Seems 'Corporate' mistakenly circulated only the first page of 'spots'. The second page had my extra four.
So, instead of pass being 16/20, it was 20/24, and a lot of people had to do the course again...

 

[haruspex]

Air-bags are good, but deflate just in time for next vehicle's impact to hurl you through screen

Presumably the next impact is coming from behind, so the risk is whiplash, not a faceplant.

 

[Nik_2213]

For a 'minor' impact, yes, but a 'major' impact that rams your vehicle a lot further into the wrack is a different story...

 

[haruspex]

For a 'minor' impact, yes, but a 'major' impact that rams your vehicle a lot further into the wrack is a different story...

Yes, interesting point.