30:46

Physics for Scientists and Engineers with Modern Physics

A 5.00-kg particle starts from the origin at time zero. Its velocity as a function of time is given by

$$

\overrightarrow{\mathbf{v}}=\left(6 \mathrm{m} / \mathrm{s}^{3}\right) t^{2} \hat{\mathbf{i}}+\left(2 \mathrm{m} / \mathrm{s}^{2}\right) t \hat{\mathbf{j}}

$$

(a) Find its position as a function of time. (b) Describe its motion qualitatively. (c) Find its acceleration as a function of time. (d) Find the net force exerted on the particle as a function of time. (e) Find the net torque about the origin exerted on the particle as a function of time. (f) Find the angular momentum of the particle as a function of time. (g) Find the kinetic energy of the particle as a function of time. (h) Find the power injected into the particle as a function of time.