A particle with mass m = 2:5 is moving along a straight trajectory. The distance covered by a particle is described by the function S(t) = t^{3} + 2t^{2} ,
where t > 0 is the time.
(a) Kinetic energy E of a particle is given by E = mv^{2}/ 2 , where v is the particle speed. Find a function that describes the kinetic energy of this particle.
(b) Find kinetic energy of the particle at time t = 5.
(c) What is the distance covered by the particle by time t = 6?
(d) Find approximate value of time t when the speed of the particle is 24.
(e) Find a function that describes the acceleration of this particle.
(f) Find the acceleration of the particle at t = 8.
(g) Find the time when the acceleration of the particle is 20.