Given that P is at the origin O at time t = 0 , calculate

(i)     the displacement of P from O after 3 seconds;

(ii)     the total distance travelled by P in the first 3 seconds.

Find the time at which the total distance travelled by P is 1 m.

(i)     displacement $= \int_0^3 {v{\text{d}}t}$     (M1)

$= 0.703{\text{ (m)}}$     A1

(ii)     total distance ${\text{ = }}\int_0^3 {\left| v \right|{\text{d}}t}$     (M1)

$= 2.05{\text{ (m)}}$     A1

[4 marks]

solving the equation $\int_0^t {\left| {\cos ({u^2})} \right|{\text{d}}u = 1}$     (M1)

$t = 1.39{\text{ (s)}}$     A1

[2 marks]