A particle moves along the x–axis during a certain time interval. Its displacement in this interval is given by Δx=4λ−9 metres, where λ is a non-zero parameter. At the end of the interval the particle is at position x2=5λ+3 metres.
(i) Obtain an expression for its initial position x1 in terms of λ.
(ii) Using λ=2, find the numerical value of x1.
(iii) For λ=2, state with reason whether the particle moved towards the positive or negative x-direction during the interval.