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=at3+bt2+48tx = at^3 + bt^2 + 48tx=at3+bt2+48t and a a\,a and b b\,b are constants.
Given that P P\,P is instantaneously at rest when t=2t = 2t=2 and when t=4t = 4t=4, find the values of a a\,a and bbb.
Given that the total distance travelled in the first T T\,T seconds is 56 m, find the value of TTT.
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.