The displacement of a particle from O O\,O is s=(14t4−2t3+4t2) ms=\left(\dfrac14t^4-2t^3+4t^2\right)\text{ m}s=(41t4−2t3+4t2) m at time t t\,t seconds, where t≥0t\geq0t≥0.
Find all the times in the interval 0≤t≤5 0\leq t\leq5\,0≤t≤5 at which the particle is instantaneously at rest.
Find the total distance travelled during the first 5 seconds.
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.