The graph below gives the velocity of a particle moving along the x-axis where t is time in seconds and v(t) is measured in meters/second. It is known that before any time passes, the particle has a position of x = 8. y (3,2) Atfter the first 5 seconds, is the particle to the right or left of where it started? Justity Your answer. Is the particle moving to the right or left at t = 37 Justify your answer. Is the particle speeding up or slowing down at t = 47 Justify your answer. Find the distance traveled by the particle after the first 5 seconds? What is the position of the particle after 3 seconds? The velocity of a particle moving along the x-axis can be represented by the function v(t). Select values of v(t) are given in the table below. It is known before any time passes the particle 1s at a position of x = 2. Time (minutes) 0 3 4 9 Velocity (feet/minute) Use a right Reimann sum with three unequal subdivisions to approximate the position of the particle after the first 9 minutes. Evaluate v(3) with the appropriate units. Approximate a(3). Is the particle speeding up or slowing down. Justify your answer. Use a left Reimann sum with n = 3 to approximate the total distance traveled in the first 9 minutes. During what interval will the particle be the farthest to the right? The problems on this page are meant to be done by hand. Conder the velocity function of a particle v(t) = t? + 6t 5 where v(t) is measured in feet per second and t is time in seconds. At t =0, is the particle speeding up or slowing down? Justify your answer. At what value(s) for t is the particle at rest? After the first 6 seconds, is the particle to the left or the right of where it started? Calculate your answer by hand. The velocity of a bug moving along the x-axis can be modeled by the function 5 1 v(t) = t*cos (Et) +2 where v(t) is in feet/second and t is time in seconds. Before any time passes, the particle has a position of x = 4. Find the distance the particle travels in the first 3 seconds. Round your answer to three decimal places. Is the particle to the right or left of where it started at t = 67 Justify your answer. Find the position of the particle the first time the particle changes directions from moving left to moving right. Round your answer to three decimal places