A particle P is projected from the origin O so that it moves in a straight line. At time t seconds after projection, the velocity of the particle, v ms^-1, is given by v = 9t2 – 63t + 90.

i. Show that P first comes to instantaneous rest when t = 2.

ii. Find the acceleration of P when t = 3.5.

iii. Find an expression for the displacement of P from O at time t seconds.

iv. Find the distance travelled by P

a. In the first 2 seconds,

b. In the first 3 seconds,