2. Suppose a particle is traveling on a one-dimensional track with velocity v(t) = t² - 6t+ 5 feet per second for 0 ≤ t ≤ 6. Further suppose that the position of the particle at time t = 0 is given by s(0) = 3 and that positive values mean the particle is traveling to the right. (a) (b) What is the position function s(t)? What is the acceleration function a(t)? (c) When is the particle at rest? The particle is at rest when the velocity is zero. Then graph the velocity function v(t).

Find the position function of a particle that travels along the x-axis for t >= 0 with acceleration of a(t)=8t-5 where the velocity at t=2 is 6 in/sec and the initial position at time t=0 is -4 inches

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Suppose that a particle moves along a straight line with acceleration defined by a(t)=t-3 where 0<t<6 (in meters per second) find the velocity and the displacement at the time t and the total distance traveled up to t=6 if v(0)=3 and d(0)=0