At time ttt seconds a particle, PPP, has position vector r\mathbf{r}r metres, with respect to a fixed origin, such that
r=(t3−4t2)i+(12t−t2)j\mathbf{r} = (t^3 - 4t^2)\mathbf{i} + (12t - t^2)\mathbf{j}r=(t3−4t2)i+(12t−t2)j
Find the exact speed of PPP when t=3t = 3t=3.
A student claims that the magnitude of acceleration of PPP will never be zero. Determine whether the student's claim is correct. Fully justify your answer.
Practise Edexcel A Level Maths Further Kinematics with exam-style questions for A Level Maths. 54 questions covering Vectors in Kinematics, Vector Methods with Projectiles, Variable Acceleration in One Dimension, Differentiating Vectors, and Integrating Vectors, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.