WHAT SHOULD YOU DO AT A YELLOW
LIGHT? (04)

Your
task: definitively prove what you should do for YOUR car, at a certain yellow
light intersection, at a given speed (Vi)
and distance (Da).

Things
you need to research:

FOR
THE INTERSECTION YOU PICK:

The
distance (Di) from the edge of the intersection, through to the other side.

The
time (Ty) from the time the light turns yellow till it turns red... (as exactly
as possible)

The
speed limit (Vsl) of the road you would travel.

YOUR
CAR:

The
length from the front bumper to the back bumper (Dcl)

The
acceleration of your car, make and model. (A) (usually given as 0-60 in ___
sec)

See
Car & Driver magazine road tests, AAA auto Guides, or research the
Internet: some links are at __http://homepage.mac.com/richtherrn/car.html__

(try
national safety board for example: http://www.nhsta.dot.gov)

The
braking deacceleration of your car make and model. (A_{B}) (usually
given as __ ft from 40 miph)

Your
reaction time (Tr) between when you see the yellow light and you can react.

You
will need to do all conversions appropriately (for example 0 to 60 miles per
hour in 10 seconds to meters per sec per sec, and 60 to 0 mph in 20 ft to
meters per sec per sec)

1
miph = 0.44704 m/s, 1 ft = .3048 meters

Hopefully you can come up with a formula for braking, dependent on
distance from intersection and speed, and one for speeding up dependent on
distance and speed and place these two inequalities on the same graph.

Safe braking is defined as when you step on the brakes and
deaccelerate at your given speed, your stopping distance is less than that
between the given distance your car and intersection. No part of your car is in
the intersection under a red light!

Safe speeding up is defined as when you speed up and accelerate at
the maximum for your given speed, you go the given distance between your car
and the intersection, plus the distance of the intersection, plus the length of
your car, and the time it takes you to do so is less than the time of the
yellow light, so that no part of your car is in the intersection under a red
light! Oh, also the maximum speed attained cannot go over the speed limit.

So
for braking : distance traveled d

f(v)=d,
so that d<Da

for
speeding up f(v)=d,
so that for t=Ty. d>Da +Di + Dcl and Vf<Vmax

All conversions should be built in as constants... Find out if
there is ever a case when you could choose to do either, or a case when you are
in trouble (you can’t safely do either!) BE CLEAR AND NEAT!!!!!

HONORS:
Find the two mathematical inequality relationships that account for ALL the
variables and plot them on a speed vs. distance away graph for that particular
car, driver and intersection.

And
make sure to write conclusions!

ACADEMIC:
List for about ten different distances away and speeds what should be done for
that particular car, driver and intersection, and show why. (Ignore speed
limit). Find the answers asked for: at a particular speed what is the minimum
safe accelerating distance, maximum safe braking?

And
make sure to write conclusions!

__BRAKING
CASE:__

we don’t
care about time, or the length of the car.

Your
distance traveled will be your car’s velocity times your reaction time plus the
rest of the distance traveled will be given by your car’s braking
deacceleration (converted to m/s^2), and your car’s initial velocity. This
total distance should be LESS than the distance from the car to the
intersection.

Distance
traveled is d = Dreaction + D
braking << Da

Dreaction=ViTr

Dbraking
= Vi^{2}/(2 A_{B})

__ACCELERATING
CASE:__

In
the time of the yellow light your car must travel MORE than the distance from
the car to the intersection PLUS the distance across the intersection PLUS the
length of the car.

Your
distance traveled will be your car’s velocity times your reaction time plus the
distance traveled as your car accelerates up to the speed limit, given by the
initial velocity, the car’s acceleration (converted to m/s^2), and the time of
the yellow light left, then plus the distance your car travels while at the
speed limit. A distance time, and velocity time graph of this case might be:

D V

T T

Distance
traveled is

D
reacting =
Vi
Tr PLUS

D
accelerating Vi
T + 1/2 A T^{2}
(Time left in yellow light) PLUS

D
at speed limit VslT (ignore for academic, )

Dtraveled
has to be more than Da + Di + Dcl
so Da < D traveled - Di - Dcl

(**HONORS:
Critical Velocity is speed at which car will reach speed limit in time of
yellow light)

EXAMPLE ANSWER TO TEST YOURSELF:

A 3 meter car that goes 0-60 in 12 seconds, and brakes from 60 mph in 180 feet, with a driver reaction time of 0.2 seconds. The car is traveling 30 mph in a 45 mph zone, 25 meters away from an intersection that is 12 meters across with a 2 second yellow light.

This driver is stuck... would have to be closer than 15.2
meters to speed up in time, and farther than 23.9 meters away to brake in time
legally! In fact, in this situation, there is ALWAYS a range of distances for a
given speed in which the driver can’t brake, and can’t speed through the
intersection in time, even with NO speed limit!L

NAME________________

DATA:

Car
Year _________ Make __________
Model_________

Car
Length in meters (Dcl) ___________________

------------------------------------

Car Year _________ Make __________ Model_________

Acceleration
0 to 60 mi p h in ______ sec. (T_{60})

A
= (Vf-Vi)/T when Vi is zero so A = .44704 (60 miph) / T_{60}

Car Acceleration in m/s^{2}
: (A) ___________

---------------------------------------------

Car Year _________ Make __________ Model_________

Braking
deacceleration from 60 mi p h in feet. ________ ft (D_{60})

Vf^{2}= Vi^{2}
+ 2 A D so A = - Vi^{2}/2D

A_{B} = (.44704 * 40)^{2} / ( 2* .3048*
D_{60})

Car Braking
Acceleration in m/s^{2}
: (A_{B}) ___________

-----------------------------------------------------------------------------------------------------------

Reaction
Time (Tr) in seconds_________________ (from class T = sqrt(2D/g) )

-----------------------------------------------------------------------------------------------------------

Intersection
LOCATION:

Intersection
Length in meters (Di)______________

Yellow
light time in seconds (Ty) ______________

Speed
Limit on Road ( Vsl) in m/s ____________

*** USE THIS DATA TO ANSWER QUESTIONS!!!

**All conversions should be built in as constants... Find out if
there is ever a case when you could choose to do either, or a case when you are
in trouble (you can’t safely do either!) BE CLEAR AND NEAT!!!!!

** HONORS:** Find the two mathematical
inequality relationships that account for ALL the variables and plot them on a
speed vs. distance away graph for that particuliarr car, driver and
intersection.

*And
make sure to write conclusions!*

** ACADEMIC:** List for about ten different
distances away and speeds what should be done for that particuliarr car, driver
and intersection, and show why. (ignore speed limit). Find the answers asked
for: at a particuliarr speed what is the minimum safe accelerating distance,
maximum safe braking?

*And
make sure to write conclusions!.......*

°Traveling
at the speed limit, (and other speeds) what is the farthest away safe braking
distance for your car?

°Traveling at the speed limit, (and other speeds) what is the closest safe accelerating distance for your car?

°Is there a speed and distance at which it is not safe to do either??? SHOW WORK!!!!

°Is there an intersection which by its nature is typically “unsafe”?

°How could this data be useful? What should we do with this
data? °How has doing this project made you think about physics and driving, and
your own driving habits?

ACADEMIC (don’t worry about values over speed limit):

Initial Speed_____ (mi ph) = __________ m/s

Reaction Distance______ Braking distance__________ Distance to be safe_______

Reaction Distance______ Accelerating distance_____ Distance to be safe_______

WORK:

Initial Speed_____ (mi ph) = __________ m/s

Reaction Distance______ Braking distance__________ Distance to be safe_______

Reaction Distance______ Accelerating distance_____ Distance to be safe_______

WORK:

Initial Speed_____ (mi ph) = __________ m/s

Reaction Distance______ Braking distance__________ Distance to be safe_______

Reaction Distance______ Accelerating distance_____ Distance to be safe_______

WORK:

Initial Speed_____ (mi ph) = __________ m/s

Reaction Distance______ Braking distance__________ Distance to be safe_______

Reaction Distance______ Accelerating distance_____ Distance to be safe_______

WORK:

ACADEMIC (don’t worry about values over speed limit):

Initial Speed_____ (mi ph) = __________ m/s

Reaction Distance______ Braking distance__________ Distance to be safe_______

Reaction Distance______ Accelerating distance_____ Distance to be safe_______

WORK:

Initial Speed_____ (mi ph) = __________ m/s

Reaction Distance______ Braking distance__________ Distance to be safe_______

Reaction Distance______ Accelerating distance_____ Distance to be safe_______

WORK:

Initial Speed_____ (mi ph) = __________ m/s

Reaction Distance______ Braking distance__________ Distance to be safe_______

Reaction Distance______ Accelerating distance_____ Distance to be safe_______

WORK:

Initial Speed_____ (mi ph) = __________ m/s

Reaction Distance______ Braking distance__________ Distance to be safe_______

Reaction Distance______ Accelerating distance_____ Distance to be safe_______

WORK:

Honors: Show work for each speed…. State whether it is below the critical velocity, above, or above speed limit.

Dist Acc if Vi<Vcrit Dreact+Dacc

Dist Acc if Vi>Vcrit Dreact+Dacc+Dat speed limit (time is time to accelerate)

Dist if Vi> SL D=VslTy

SPEED DISTANCE away to Brake? Accelerate?

FUNCTION:

BRAKING Da > f ( Vi)

ACCELERATING Da < f (Vi)

GRAPH: