(Solved): particle moves according to a law of motion s=f(t),t0, where t is measured in seconds an ...

particle moves according to a law of motion $$s=f(t),t?0$$, where $$t$$ is measured in seconds and $$s$$ in feet. $$f(t)=0.01t^4?0.03t^3$$ (a) Find the velocity at time $$t$$ (in $$\mathrm{ft}/\mathrm{s}$$ ). $$v(t)=$$ (b) What is the velocity after $$2\mathrm{s}$$ ? $$v(2)=$$ (c) When is the particle at rest? $$\begin{array}{ll}t=& \text{ s (smaller value) }\\ t=& \text{ s (larger value) }\end{array}$$ (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Find the total distance traveled during the first 9 s. (Round your answer to two decimal places.) $$\mathrm{ft}$$ (f) Find the acceleration at time $$t$$ (in $$\mathrm{ft}/{\mathrm{s}}^2)$$. $$a(t)=$$ Find the acceleration after $$2\mathrm{s}$$. $$a(2)=\mathrm{ft}/{\mathrm{s}}^2$$ (g) Graph the position, velocity, and acceleration functions for the first $$9\mathrm{s}$$.