AQA
Paper 2
2022
June
Q17
7 marks
Standard +0.8
17 A particle is moving such that its position vector, \(\mathbf { r }\) metres, at time \(t\) seconds, is given by
$$\mathbf { r } = \mathrm { e } ^ { t } \cos t \mathbf { i } + \mathrm { e } ^ { t } \sin t \mathbf { j }$$
Show that the magnitude of the acceleration of the particle, \(a \mathrm {~ms} ^ { - 2 }\), is given by
$$a = 2 \mathrm { e } ^ { t }$$
Fully justify your answer.
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