Solved: CALC A turtle crawls along a straight line, which

Chapter 2, Problem 2.15

(choose chapter or problem)

A turtle crawls along a straight line, which we will call the x-axis with the positive direction to the right. The equation for the turtle's position as a function of time is \(x(t)=50.0\mathrm{\ cm}+(2.00\mathrm{\ cm}/\mathrm{s})t-\left(0.0625\mathrm{\ cm}/\mathrm{s}^2\right)t^2\). (a) Find the turtle's initial velocity, initial position, and initial acceleration. (b) At what time t is the velocity of the turtle zero? (c) How long after starting does it take the turtle to return to its starting point? (d) At what times t is the turtle a distance of 10.0 cm from its starting point? What is the velocity (magnitude and direction) of the turtle at each of these times? (e) Sketch graphs of x versus t, \(v_{x}\) versus t, and \(a_{x}\) versus t, for the time interval t = 0 to t = 40 s.