A particle P P\,P moves in a straight line so that, at time t t\,t seconds, its acceleration a m s−2a \text{ m s}^{-2}a m s−2 is given by
a={4t−t20≤t≤327t2t>3 a = \begin{cases} 4t - t^2 & 0 \leq t \leq 3 \\ \frac{27}{t^2} & t > 3 \end{cases} a={4t−t2t2270≤t≤3t>3At t=0t = 0t=0, P P\,P is at rest.
Find the speed of P P\,P when t=3t = 3t=3.
Find the speed of P P\,P when t=6t = 6t=6.
28 exam-style questions on Edexcel AS 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.