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University Physics with Modern Physics

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 cm + (2.00 cm/s)$t -$ (0.0625 cm/s$^2)t^2$. (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 those 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.