The position of a particle moving on a straight line is given by x=10t−t2 (in metres) for 0≤t≤10s, where t is in seconds. The positive x-direction is taken to the right.
(i) Obtain expressions for the velocity v(t) and the acceleration a(t) of the particle.
(ii) At what instants is the particle momentarily at rest? For each such instant, state whether the particle is about to move in the positive or the negative x-direction immediately afterwards.
(iii) Calculate the total distance travelled by the particle in the first 10s.
(iv) Determine at what time(s), if any, the particle is back at the origin within the given interval.