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69. (a) With length in centimeters and time in seconds, we have
u
=
dy
dt
=
−
60
π
cos
³
πx
8
−
4
πt
´
.
Thus, when
x
=6and
t
=
1
4
,weobta
in
u
=
−
60
π
cos
−
π
4
=
−
60
π
√
2
=
−
133
so that the
speed
there is 1
.
33 m/s.
(b) The numerical coeﬃcient of the cosine in the expression for
u
is
−
60
π
. Thus, the maximum
speed
is 1
.
88 m/s.
(c) Taking another derivative,
a
=
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics

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