Magnitude of acceleration at given time

A question is this type if and only if the task specifically requires computing the magnitude (scalar value) of the acceleration vector at a particular time t, distinct from finding the force or the full acceleration vector.

2 questions · Moderate -0.4

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Edexcel M2 2012 June Q1
10 marks Moderate -0.5
  1. \hspace{0pt} [In this question \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular unit vectors in a horizontal plane.]
A particle \(P\) moves in such a way that its velocity \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\) at time \(t\) seconds is given by $$\mathbf { v } = \left( 3 t ^ { 2 } - 1 \right) \mathbf { i } + \left( 4 t - t ^ { 2 } \right) \mathbf { j }$$
  1. Find the magnitude of the acceleration of \(P\) when \(t = 1\) Given that, when \(t = 0\), the position vector of \(P\) is i metres,
  2. find the position vector of \(P\) when \(t = 3\)
OCR MEI Further Mechanics Major Specimen Q1
4 marks Moderate -0.3
A particle P has position vector \(\mathbf{r}\) m at time \(t\) s given by \(\mathbf{r} = (t^3 - 3t^2)\mathbf{i} - (4t^2 + 1)\mathbf{j}\) for \(t \geq 0\). Find the magnitude of the acceleration of P when \(t = 2\). [4]