A particle P P\,P travels along a straight line through a point OOO.
At time t t\,t seconds, t≥0t \geq 0t≥0, after passing through O O\,O the displacement of P P\,P from O O\,O is r r\,r metres, where r=t2(4t2−4t+1)r = t^2(4t^2 - 4t + 1)r=t2(4t2−4t+1)
Show that P P\,P never moves onto the negative side of OOO.
Find the times at which P P\,P is instantaneously at rest.
Find the total distance travelled by P P\,P in the interval 0≤t≤50 \leq t \leq 50≤t≤5.
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.