Forces in vector form: resultant and acceleration

A single force of magnitude 4 newtons acts on a particle of mass 50 grams. Find the magnitude of the acceleration of the particle. Circle your answer. [1 mark] \(12.5 \text{ m s}^{-2}\) \(\quad\) \(0.08 \text{ m s}^{-2}\) \(\quad\) \(0.0125 \text{ m s}^{-2}\) \(\quad\) \(80 \text{ m s}^{-2}\)

Three forces \(\mathbf{L}\), \(\mathbf{M}\) and \(\mathbf{N}\) are given by $$\mathbf{L} = 2\mathbf{i} + 5\mathbf{j},$$ $$\mathbf{M} = 3\mathbf{i} - 22\mathbf{j},$$ $$\mathbf{N} = 4\mathbf{i} - 23\mathbf{j}.$$ Find the magnitude and direction of the resultant of the three forces. [6]

Two forces \(\mathbf{F}\) and \(\mathbf{G}\) acting on an object are such that $$\mathbf{F} = \mathbf{i} - 8\mathbf{j},$$ $$\mathbf{G} = 3\mathbf{i} + 11\mathbf{j}.$$ The object has a mass of 3 kg. Calculate the magnitude and direction of the acceleration of the object. [7]