Chapter 11.1, Problem 11.25P

The acceleration of a particle is defined by the relation $a=-k{v}^{2.5}$ , where k is a constant. The particle starts at $x=0$ with a velocity of 16 mm/s, and when $x=6$ mm the velocity is observed to be 4 mm/s. Determine (a) the velocity of the particle when $x=5$ mm (b) the time at which the velocity of the particle is 9 mm/s.