FREE
RESPONSE
Police
use
a
formula
to
estimate
the
speed
a
car
was
traveling
before
an
accident
by
measuring
its
skid
marks.
Function
S
is
used
to
model
the
speed
the car
was
traveling
in
mph
where
d
is
the
distance
the
car
skidded
in
feet
and
f
is
the
coefficient
of
friction
which
depends
on
the
road
surface and
road
conditions.
S(d)
=
/30df
a.
A
country
road
has
a
coefficient
of
friction
of
0.9
when
it
is
dry
and
0.4
when
it
is
wet.
What
values
of
distance
skidded
would
you
expect
in
both
conditions
for
a
car
that
was
travelling 110
mph when
the
brakes
were
applied?
110
=
,/30d(0.9)
110
=
/30d(0.4)
d
=
448.148
feet
d
=
1008.333
feet
b.
Analyze
the
rate
of
change
from
a
measured
70-foot
skid
mark
to
a
160-foot
skid
mark
on
the
dry
country
road.
S$(70)
=,/30(70)(0.9)
65.727-43.474
_
22.253
=
(.247
mph
per
foot
of
skid
mark
5(160)
=
,/30(160)(0.9)
160—70
90
pap
c.
The
distance
of
a
skid
mark
is
inversely
proportional
to
the
product
of
30
and
the
coefficient
of
friction.
Using
the
60-foot
skid
mark
on
a
dry
country
road,
find
the
constant
of
proportionality.
Explain
what
it
means
in
this
context.
d
=
%
s
=
/30d(0.9)
k
52
=30d(0.9)
60
=
30(0.9)
$%
=30d(0.9)
k
=
1620
52
;
30(0.9)
k
52
30(0.9)
30(0.9)
k
is
speed?
so
the
speed
is
Vk
©
The
Algebros
from
FlippedMath.com
