A particle switches from a curve to its normal

A particle is moving along a curve, $C$, such that its position at time $t$ seconds after it is set into motion is given by the parametric equations $x=t+e^{-2t}$, $y=t-e^{-2t}$.

(i) State the coordinates of the initial position of the article.1 mark

(ii) Explain what would happen to the path of the particle after a long time.1 mark

At the time of 2 seconds after the particle was set into motion, an external force struck the particle resulting in the particle moving in a straight line along the normal to the path at the point of collision.

(iii) Find an equation for the normal to the curve $C$ at the point $t=2$, leaving your answer correct to 3 decimal places.3 marks

After $T$ seconds, where $T>2$, the particle reaches point $A$, which lies on the $x$-axis, and stops moving.

(iv) Find the coordinates of the point $A$. Hence, give a sketch of the path traced by the particle, indicating the coordinates of any axial intercepts.4 marks

(v) Find the total area bounded by the path of the particle in the first $T$ seconds and the positive $x$-axis.4 marks

[2017/SRJC/Prelim/I/10]