A particle P P\,P moves on the x x\,x axis. The acceleration of P P\,P at time t t\,t seconds, t≥0t \geq 0t≥0, is (3t+5) m s−2(3t + 5) \text{ m s}^{-2}(3t+5) m s−2 in the positive x x\,x direction. When t=0t = 0t=0, the velocity of P P\,P is 2 m s-1 in the positive x x\,x direction. When t=Tt = Tt=T, the velocity of P P\,P is 6 m s-1 in the positive x x\,x direction.
Show that the velocity of P P\,P at time t t\,t seconds is v=32t2+5t+2\displaystyle v = \frac{3}{2}t^2 + 5t + 2v=23t2+5t+2.
Hence 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.