A particle P P\,P moves in a straight line such that at t t\,t seconds, t≥0t \geq 0t≥0, its displacement, s ms \text{ m}s m, from its starting point is given by:
s=12t−23t3 s = 12t - \frac{2}{3}t^3 s=12t−32t3the velocity of P P\,P at t t\,t seconds,
the value of t t\,t when P P\,P changes direction of motion,
the value of t t\,t at the instant P P\,P returns to its starting point.
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.