Chapter 2, Problem 70PQ

A dancer moves in one dimension back and forth across the stage. If the end of the stage nearest to her is considered to be the origin of an x axis that runs parallel to the stage, her position, as a function of time, is given by

$\stackrel{\to }{x}\left(t\right)=\left[\left(0.02\text{m}/{\text{s}}^{\text{3}}\right)t^3-\left(0.35\text{m}/{\text{s}}^{\text{2}}\right)t^2+\left(1.75\text{m}/\text{s}\right)t-2.00\text{m}\right]\hat{i}$

1. a. Find an expression for the dancer’s velocity as a function of time.
2. b. Graph the velocity as a function of time for the 14 s over which the dancer performs (the dancer begins when t = 0) and use the graph to determine when the dancer’s velocity is equal to 0 m/s.