A particle is moving along a straight trajectory. The distance covered by a particle is described by the function S(t) = 2t^3 + 5t^2 , where t > 0 is the time.

a)What is the distance covered by the particle by time t = 4 ?

b)Find approximate value of time t when the speed of the particle is 84

c)Find a function that describes the acceleration of this particle.

d)Find the acceleration of the particle at t = 5

e)Find the time when the acceleration of the particle is 46