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Re: oops! help!



General solution:

The distance the car will travel with reaction time (no acceleration) is
s[1]=v[1] x t[1] where t[1] is the reaction time and v[1] is the
initial velocity of the car.

The total distance traveled will be s[2]=s[1] + v[1] x t[2] + 1/2 x a x
t[2]^2 where t[2] is the time to stop and a is the acceleration.

With average acceleration a = (v[3] - v[2])/t[2] where v[3] = 0 if
the car stops. Substituting 0 for v[3] and solving for t[2] we get

t[2] = -v[1]/a a needs to have a sign opposite v[1] if the car is to
stop (other wise it will go faster).

Substituting t[2] into the total distance equation gives s[2] = v[1] x
t[1] + v[1] x (-v[1]/a) + 1/2 x a x (-v[1]/a)^2

simplifying gives s[2] = v[1] x t [1] - v[1]^2/a + v[1]^2/(2 x a)

combining the v[1]^2 terms gives s[2] = v[1] x t[1] + -v[1]^2 / (2 x a)
which is a quadratic equation to solve for v[1]

Setting the equation to 0 gives 0 = A x v[1]^2 + B x v[1] + C where A
= -1/(2 x a) , B = t[1] and C = -s[2]

For your data, s[2] = 48.78 m, a = -5.18 m/s^2 and t[1 alert] = 1.6 s
v[1] = 15.67 m/s (or -32.247 m/s). The car will travel 25.07 m during
the 1.6 sec reaction time and 23.70 meters additional to stop (too many
sig figs when starting with 160 feet) (you can calculate this distance
by using (0^2 - (15.67m/s)^2)/(2 x -5.18m/s^2)

For s[2] = 48.78 m, a=-5.18 m/s^2 and t[1 unfocused] = 2.5 s, v[1] = 12
m/s (or -39 m/s)

Julie Hilsenteger wrote:

Oops! I forgot to change the subject on my e-mail and figured that some may
not even look at. So I am sending it again with an apology. I couldn't get
my mailer to mail correctly so I opened an old one and used the forward
function. Thank you anybody for any help.



Helllllp! I was only peripherally paying attention to Tina Fanetti's
question for help on the University Physics problem but did read Larry
Woolf's data and his politically correct problem. I decided to put the
problem on a test late last night. I e-mailed Larry for help but haven't
heard back yet and am getting desperate and hoping one of you will grace me
with some assistance. Here is the e-mail I sent him:

Hi,
I need help because I seem to be having a brain fart. I just put on my test
for my advanced physics students a problem based on the one you cited, I


just


changed things to meters though. Here is the problem:
Headlights illuminate the road up to 48.78 m (which is 160 feet) in front of
you. You are driving along and see a stop sign. What is the fastest speed
you can drive and still stop safely at night? Your reaction time is divided
into a perception time ("I need to brake") and a movement reaction time
(movement of the foot). For alert drivers, the average reaction time is 1.6
second. For drivers encountering an unexpected obstacle around a blind


curve


or not really focusing on the road, an average reaction time is closer to


2.5


seconds. Calculate the fastest speed for both an alert driver and unfocused
driver. The average deceleration of a car is 5.18 m/s^2.

OK, I cannot seem to get it. I know that for the reaction time part the car
is going constant velocity and covers a distant dependent on the velocity.
Then the car brakes and ends with a final velocity of zero. But all I know
is the total distance the car is allowed to go, the acceleration, the final
velocity. The initial velocity for the braking part is the velocity for the
reaction time part and the distance traveled braking is the 48.78m -


distance


traveled during the reaction time part. I seem to have too many unknowns.
So, how do you solve it?

It's my bad for blindly putting it on the test last night and not working it
out before the class sat down to take the test, but as I quickly typed it in
after a crosscountry meet, I just assumed I (and most students) would have


no


problem. Can you give us a hand here so that I can set myself and students
straight? Thank you so much!





--
Julie Hilsenteger
Physics Teacher
Centennial High School
3505 SE 182nd
Gresham, OR 97030
503-661-7612
julie_hilsenteger@centennial.k12.or.us




--
Arlyn DeBruyckere
Science Teacher
Hutchinson High School
1200 Roberts Road
Hutchinson, MN 55350
320-587-2151
mailto:arlynd@hutch.k12.mn.us
http://www.hutch.k12.mn.us
http://www.hutch.k12.mn.us/teacher/ArlynDeBruyckereHS.cfm

HEA Website http://www.angelfire.com/mn3/hea