Rates and Integration
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The hose from a fire truck is gradually turned off, so that the volume of water, \(V\) litres, in the truck at time \(t\) seconds changes at the rate \(\dfrac{d V}{d t}=\dfrac{t}{2}-3\).
(i) At what time was the hose fully turned off?
(ii) Find \(V\) as a function of \(t\) if the truck contained 145 L of water after 2 seconds.
(iii) Hence or otherwise, find the total volume of water that is released during the time the hose is turned off.
i) \(6 \text{ seconds}\)
ii) \(V =\dfrac{t^2}{4}-3 t+150\)
iii) \(9\text{ L of water released.}\)
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