A particle P P\,P travels along a straight line through a point O O\,O so that at time t t\,t s after passing through O O\,O its displacement from O O\,O is x x\,x m, where x=2t3−18t2+ktx = 2t^3 - 18t^2 + ktx=2t3−18t2+kt, where k k\,k is a constant satisfying 30<k<5430<k<5430<k<54
the times when P P\,P is instantaneously at rest, in terms of kkk,
the total distance travelled in the first 5 seconds, in terms of kkk.
308 exam-style questions on Edexcel A Level Maths Variable Acceleration, covering 11.1 Functions of Time, 11.2 Using Differentiation, 11.3 Maxima and Minima Problems, 11.4 Using Integration, and 11.5 Constant Acceleration Formulae. Each one has a worked solution and a mark scheme showing where the marks go.