Forces in vector form: kinematics extension

Forces are given in i,j (or column vector) form and the question extends into kinematics, requiring position, velocity or speed at a given time using constant-acceleration equations in vector form.

26 questions · Moderate -0.4

3.03d Newton's second law: 2D vectors
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Pre-U Pre-U 9794/2 2010 June Q11
10 marks Standard +0.3
Two forces \(\mathbf{F}_1\) and \(\mathbf{F}_2\) are given by $$\mathbf{F}_1 = 13\mathbf{i} + 4\mathbf{j} - 3\mathbf{k}, \quad \mathbf{F}_2 = -2\mathbf{i} + 6\mathbf{j} + \mathbf{k},$$ in which the units of the components are newtons. A third force, \(\mathbf{F}_3\), of magnitude 6 N acts parallel to the vector \(2\mathbf{i} - 2\mathbf{j} + \mathbf{k}\).
  1. Find the two possible resultants of \(\mathbf{F}_1\), \(\mathbf{F}_2\) and \(\mathbf{F}_3\), and show that they have the same magnitude. [5]
A particle, \(P\), of mass 2 kg is initially at rest at the origin. The only forces acting on \(P\) are \(\mathbf{F}_1\) and \(\mathbf{F}_2\).
  1. Find the magnitude of the acceleration of \(P\). [3]
  2. Find the time taken for \(P\) to travel 60 m. [2]