In this question i and j are the unit vectors due east and north respectively. A cyclist makes a journey between two points A and B. At time t=0s the cyclist is moving due east at 2ms^(-1). The cyclist is modelled as a particle. Relative to A, the position vector of the cyclist at time t seconds is r metres. Given that the acceleration of the cyclist is constant and equal to 0.2i-0.8jms^(-2), find:
a) the position vector of the cyclist after 10 seconds
b) the distance of the cyclist from A after 10 seconds. After 10 seconds the cyclist stops accelerating and heads due east at a constant speed of 5ms^(-1).
c) Find the value of t when the cyclist is directly south-east of A. After a further 30s the cyclist reached point B.
d) Work out the bearing of B from A to the nearest degree.

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