Particle moving perpendicular to vector

A question is this type if and only if the task requires finding the time when the velocity vector is perpendicular to a given vector (or axis), by setting the dot product of velocity with that vector equal to zero.

1 questions · Moderate -0.3

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OCR MEI Further Mechanics Major 2020 November Q4
10 marks Moderate -0.3
A particle P moves so that its position vector \(\mathbf{r}\) at time \(t\) is given by $$\mathbf{r} = (5 + 20t)\mathbf{i} + (95 + 10t - 5t^2)\mathbf{j}.$$
  1. Determine the initial velocity of P. [3] At time \(t = T\), P is moving in a direction perpendicular to its initial direction of motion.
  2. Determine the value of \(T\). [3]
  3. Determine the distance of P from its initial position at time \(T\). [4]