Rates and Integration
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The hose from a fire truck is gradually turned off, so that the flow rate of water ( \(V\) litres) from the hose at time ( \(t\) seconds) is given by \(\dfrac{d V}{d t}=\dfrac{t}{2}-3\).
(i) At what time was the hose fully turned off?
(ii) Find \(V\) as a function of \(t\) if the truck contained 145L 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) \(9 L \text { of water released. }\)
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