I really can't understand what's wrong with my physics calculations...can someone verify them?

Question

Here's the problem: "A motorist is traveling at 18.0 m/s when he sees a deer in the road 38.0 miles ahead. If the maximum negative acceleration of the vehicle is -4.5 m/s, what is the maximum reaction time (delta)t of the motorist that will allow him to avoid hitting the deer?

Now when I do my calculations, I get:
vi = 18.0 m/s
vf = ?
t = ?
a = -4.5 m/s^2
d = 38.0 m

d = vit + 1/2at^2
38.0 = 18t + (-2.25)t^2
2.25t^2 - 18t + 38.0 = 0

Then put into quadratic formula....which gives out a negative root...
So doesn't that mean the driver can't avoid hitting the deer?

Answer 1

I'm not 100% sure about the way the question is worded, and I wouldn't want to mislead you.

But, try treating the acceleration as positive, since acceleration is symmetrical and you would travel the same distance whether accelerating or decelerating at the same rate, and then solve

2.25t² + 18t - 38 = 0

in which case,

t = -9.73488s or t = 1.73488s

Since the negative answer doesn't seem to apply,
then perhaps t = 1.735s is the answer you need.

The way epidavros answered the question makes me wonder if I interpreted it correctly. I simply attempted to solve your quadratic from a symmetric point of view. Questions like this drive me bonkers. Computing planet orbits is easier. But I've been awake for over 20 hours, so maybe I'm really dreaming all this.

LOL
 

Answer 2

Simplest way to think through this:

How long does it take him to stop -
t = v/a = 18/4.5 = 4 secs

How far does he travel in this time -
s = ut + 1/2 at^2 = 18x4 + 1/2 x -4.5 x 4^2 = 36 m

So if the deer is 38 m ahead he must react within 2 m.

How long does this give him -
t = 2/18 = 1/9 sec.

Answer 3

Something wrong in the QUESTION:
The deer is 38.0 MILES ahead

I would assume the deer is 38 METERS ahead
Time to stop:
t = v/a = 18/4.5 = 4 secs
Distance to stop:
d = (a * t^2) / 2 = (18 * 4^2) / 2 = 144m
He has only 38m to stop.
He will hit the deer, full stop.
(dont drive so fast!)
Now, assume 38 MILES ahead
38 miles = 38 * 1600 = 60800m
He will miss the deer: he needs only 144m to stop.

Something wrong with your question!

Answer 4

No, not something is incorrect. Physics is appropriate in our every day existence. There are particularly complicated matters in Physics. yet, in case you will learn nicely you will comprehend it. Memorize the formula. observe it. try a topic. Physics is relaxing!