4.2 Exercise 8

The position of a particle for t > 0 is given by $\overset{\rightarrow}{r} \left(t\right) = \left(3.0 t^{2} \hat{i} - 7.0 t^{3} \hat{j} - 5.0 t^{−2} \hat{k}\right) \text{m} .$ (a) What is the velocity as a function of time? (b) What is the acceleration as a function of time? (c) What is the particle’s velocity at t = 2.0 s? (d) What is its speed at t = 1.0 s and t = 3.0 s? (e) What is the average velocity between t = 1.0 s and t = 2.0 s?