6 The volume of water (in litres) which has owed through a swimming pool lter 1' 4 minutes after starting it is V = (30:3 '1) where 0 s t s 90. a At what rate is water owing through the lter at any time, I? b Sketch a graph of (rid1: over the domain [0, 90]. c When is the rate of ow greatest? 7 A particle moves in a straight line so that its displacement from a point, 0, at any time, t, is x = 43:2 + 4. Find: a the velocity as a function of time b the acceleration as a function of time c the velocity and acceleration when t = 2. Chapter 3 Applications of differentiation 337 8 If a particle is moving in a straight line so that its displacement from the origin at any time, t, is x = r3 12:2 + 36:, nd: a the velocity b the time and displacement when the velocity is zero It the acceleration when the velocity is zero