A motorboat starts from rest with an acceleration given by the law \( a=\frac{c}{(x+4)^{2}} \mat...

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A motorboat starts from rest with an acceleration given by the law \( a=\frac{c}{(x+4)^{2}} \mathrm{~m} / \mathrm{s}^{2} \), where \( c \) is a positive constant. Given that the velocity of the boat when its displacement is \( 8 \mathrm{~m} \) is \( 4 \mathrm{~m} / \mathrm{s} \). Find:
(a) The magnitude of \( c \).
(b) The position of the boat when its speed was \( 4.5 \mathrm{~m} / \mathrm{s} \).
(c) The maximum velocity of the boat.
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