M1 south-east direction position vectors

Relative to a fixed origin O , the horizontal unit vectors i and j are pointing due east and due north, respectively. A particle P is moving with constant acceleration of (0.25 0.5 i j − ) 2 ms− . It is initially observed passing through the point with position vector (2 3 i j − ) m with velocity of (i j + 3.5 ) 1 ms− .

a) Find an expression for the velocity of P , t s after it was first observed.

b) Determine an expression for the position vector of P , t s after it was first observed.

c) Calculate the distance of P from the origin O , when P is moving in a southeastern direction.

Hi, I have done the first two parts of this question and got the right answer which is (2+t+0.125t^2)i + (-3+3.5t-0.25t^2)j . For part c, since its a south-east direction, surely the j components will switch signs and this new vector will be equal to the i vectors and you solve for t. For this I got t= 35.8s however the right answer should be t=18. Thanks. ( this video shows an example of how to tackle it http://www.examsolutions.net/a-level-maths-papers/worked-solution/worked-solution.php?paper_id=55&solution=7.4