A particle moves in a straight line. Its acceleration is a=4t−t2a=4t-t^2a=4t−t2 for 0≤t≤30\leq t\leq30≤t≤3, and a=27t2a=\dfrac{27}{t^2}a=t227 for t>3t>3t>3, where a a\,a is measured in m s−2\text{m s}^{-2}m s−2. The particle is at rest at t=0t=0t=0.
Find the speed at t=3t=3t=3.
Find the speed at t=6t=6t=6.
260 exam-style questions on OCR A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Displacement-time and velocity-time graphs, 3.2.4 Constant acceleration formulae, 3.2.5 Constant acceleration in two dimensions (A-level only), 3.2.6 Non-uniform acceleration in one dimension (A-level only), 3.2.7 Non-uniform acceleration in two dimensions (A-level only), 3.2.8 Motion under gravity using vectors (A-level only), and 3.2.9 Projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.