Final answer:
The velocity of the particle as a function of time is v(t) = 3t^2 − 3, and the acceleration as a function of time is a(t) = 6t.
Step-by-step explanation:
The equation of motion of a particle is given by s(t) = t3 − 3t, where s is in meters and t is in seconds. To find the velocity and acceleration as functions of time, we take the derivatives of the position function s(t).
Velocity as a function of time is the first derivative of position with respect to time. So, v(t) = ds/dt = 3t2 − 3. Acceleration is the derivative of velocity with respect to time, therefore a(t) = dv/dt = 6t.