A particle moves in a straight line so that at time t t\,t seconds, t≥0t \geq 0t≥0, its velocity is v=(at2+bt)v = (at^2 + bt)v=(at2+bt) m s−1^{-1}−1 where a a\,a and b b\,b are constants.
The acceleration of the particle when t=1t = 1t=1 is 4 m s−2^{-2}−2.
The particle is instantaneously at rest when t=3t = 3t=3.
Find the value of a a\,a and the value of bbb.
Find the maximum velocity of the particle.
265 exam-style questions on AQA A Level Maths 3.2 Q: Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Constant acceleration formulae, 3.2.4 Calculus in kinematics (A-level only), and 3.2.5 Motion under gravity and projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.