5.
Calculus
in
the
Physical
World,
2UA
2008
HSC
6b
6.
Calculus
in
the
Physical
World,
2UA
2015
HSC
14a
The
graph
shows
the
velocity
of
a
particle,
¥
metres
per
second,
as
a
function
of
time,
¢
In
a
theme
park
ride,
a
chair
is
released
from
a
height
of
110
metres
and
falls
vertically.
seconds.
Magnetic
brakes
are
applied
when
the
velocity
of
the
chair
reaches
—37
metres
per
second.
20
Lt
110m
)
T"
l
,
I
E
:
?
————
Magnetic
brakes
NOT
TO
o
2
4
6
b
12
4
SCALE
(i)
Whatis
the
initial
velocity
of
the
particle?
(1
mark)
(i)
When
is
the
velocity
of
the
particle
equal
to
zero?
(1
mark)
The
height
of
the
chair
at
time
¢
seconds
is
£
metres.
The
acceleration
of
the
chair
is
given
_
_
_
by
&
=
—
10.Atthe
release
point,
t
=
0,2
= 110
and
&
=
0.
(iif)
When
is
the
acceleration
of
the
particle
equal
to
zero?
(1
mark)
i
i
=
—
(iv)
By
using
Simpson's
Rule
with
five
function
values,
estimate
the
distance
travelled
by
()
Using
calculus,
show
that
2
5%
+
110.
(2
marks)
the
particle
between
¢
=
0
and
¢t
=
8.
(3marks)
(ii)
How
far
has
the
chair
fallen
when
the
magnetic
brakes
are
applied?
(2
marks)
7.
Calculus
in
the
Physical
World,
2UA
2014
HSC
13c
The
displacement
of
a
particle
moving
along
the
z-axis
is
given
by
A
s
where
2
is
the
displacement
from
the
origin
in
metres,
¢
is
the
time
in
seconds,
and
¢
>
0.
(i)
Show
that
the
acceleration
of
the
particle
is
always
negative.
(2
marks)
(ii)
What
value
does
the
velocity
approach
as
¢
increases
indefinitely?
(1
mark)