The equation of motion of a particle is s = 2t3 − 8t2 + 4t + 2, where s is in meters and t is in seconds. (assume t ≥ 0.) (a) find the velocity and acceleration as functions of t.

The equation of motion of a particle is given by,

s =

Let velocity of particle is denoted by v.

The velocity of the particle is given by,

velocity (v) =

v =

v =

v =

Thus, Velocity of particle is given by,

v =

Let acceleration of the particle is denoted by a.

The acceleration of particle is given by,

Acceleration =

a =

a =

a = 12t - 16

Thus, acceleration of the particle is given by,

a = 12t - 16