A particle is moving in a straight line such that its velocity, v ms^-1, t seconds after passing a fixed-point O is v = e^2t – 6e^-2t – 1.

i. Find an expression for the displacement, sm, from O of the particle after t seconds.

ii. Using the substitution u = e^2t, or otherwise, find the time when the particle is at rest.

iii. Find the acceleration at this time.