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) = t³ + 2t² ,

where t > 0 is the time.

(a) Kinetic energy E of a particle is given by E = mv²/ 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.