The position vector of a particle at time t t\,t seconds is r=(t3−6t2+9t)i+(2t2−8t)j\mathbf r=(t^3-6t^2+9t)\mathbf i+(2t^2-8t)\mathbf jr=(t3−6t2+9t)i+(2t2−8t)j metres.
Show that the velocity and acceleration are perpendicular when t=2t=2t=2.
Find all the other positive times at which the velocity and acceleration are perpendicular.
204 exam-style questions on CCEA A Level Maths 4.1 Kinematics (A-level only), covering 4.1.1 Kinematics (A-level only), 4.1.2 Kinematics (A-level only), and 4.1.3 Kinematics (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.