The position of a particle for t> 0 is given by r(t) (4.02î - 3.0t3j - 3.0t 2k) m. (a) What is the velocity as a function of time? (Express your answer in vector form. Use the following as necessary: t. Assume t is in seconds and Do not include units in your answer.) is in m/s. v(t)= (b) What is the acceleration as a function of time? (Express your answer in vector form. Use the following as necessary: t. Assume t is in seconds and a is in m/s2, Do not include units in your answer.) a(t)= (c) What is the particle's velocity at t 2.0 s (in m/s)? (Express your answer in vector form.) v(2.0 s) = m/s (d) What is its speed at t = 1.0 s and t = 3.0 s (in m/s)? v(1.0 s) m/s v(3.0 s) m/s (e) What is the average velocity between t = 1.0 s and t = 2.0 s (in m/s)? (Express your answer in vector form.) m/s