Force from vector acceleration

A question is this type if and only if it requires finding a force vector using Newton's second law (F = ma) with vector acceleration.

3 questions · Standard +0.0

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Edexcel M2 Q1
7 marks Moderate -0.5
  1. A particle \(P\) of mass 2 kg is subjected to a force \(\mathbf { F }\) such that its displacement, \(\mathbf { r }\) metres, from a fixed origin, \(O\), at time \(t\) seconds is given by
$$\mathbf { r } = \left( 3 t ^ { 2 } - 4 \right) \mathbf { i } + \left( 3 - 4 t ^ { 2 } \right) \mathbf { j }$$
  1. Show that the acceleration of \(P\) is constant.
  2. Find the magnitude of \(\mathbf { F }\).
Edexcel M2 Q3
10 marks Standard +0.3
A particle \(P\) of mass \(0.3\) kg is moving under the action of a single force \(F\) newtons. At time \(t\) seconds the velocity of \(P\), v m s\(^{-1}\), is given by $$\mathbf{v} = 3t^2\mathbf{i} + (6t - 4)\mathbf{j}.$$
  1. Calculate, to 3 significant figures, the magnitude of \(\mathbf{F}\) when \(t = 2\). [5]
When \(t = 0\), \(P\) is at the point \(A\). The position vector of \(A\) with respect to a fixed origin \(O\) is \((3\mathbf{i} - 4\mathbf{j})\) m. When \(t = 4\), \(P\) is at the point \(B\).
  1. Find the position vector of \(B\). [5]
Edexcel M2 2002 January Q3
10 marks Standard +0.3
A particle \(P\) of mass 0.3 kg is moving under the action of a single force \(\mathbf{F}\) newtons. At time \(t\) seconds the velocity of \(P\), \(\mathbf{v}\) m s\(^{-1}\), is given by $$\mathbf{v} = 3t\mathbf{i} + (6t - 4)\mathbf{j}.$$
  1. Calculate, to 3 significant figures, the magnitude of \(\mathbf{F}\) when \(t = 2\). [5]
When \(t = 0\), \(P\) is at the point \(A\). The position vector of \(A\) with respect to a fixed origin \(O\) is \((3\mathbf{i} - 4\mathbf{j})\) m. When \(t = 4\), \(P\) is at the point \(B\).
  1. Find the position vector of \(B\). [5]