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7. The data in the table gives selected values for the velocity, in meters per minute, of a particle moving along the X-axis. The velocity y is a differentiable function of time . Timer Velocity 12 -3 2 3 5 7 5 Att = 0. is the particle moving to the right or left? Justify. b. Is there a time during the time interval 0 S t s 12 minutes when the particle is at rest? Justify. c. Use the data from the table to approximate v' (10). d. Explain the meaning of v'(10) in terms of the particle motion. Let s(t) represent the position of the particle in #8. What does s(9) - s(0) represent? 8. The graph represents the velocity, in feet per second, of a particle moving along the x-axis over the time interval from t = 0 to t = 9 seconds. a. Att = 4, is the particle moving to the right What happens to the or left? Justify. distance traveled when velocity switches from positive to negative? b. Over what time interval is the particle moving left? Justify. How would you find the e. Att = 4, is the acceleration positive or displacement from 0 to 5 negative? Justify. seconds? 4. What is the average acceleration of the e. At what time t in the given interval is the particle over the interval 2 S t s 4? particle furthest to the right. Justify. What is the displacement Show the computations and label your from 5 to 9 seconds? Is it answer. positive or negative, why? 9. A particle moves along the x-axis so that at time t its position is given by x(t) = 13 - 6t2 + 9t + 11 where t is measured in seconds and x is measured in feet. How could you make it a. Att = 0, is the particle moving to the right |b. Att = 1, is the velocity of the particle positive? or left? Justify. increasing or decreasing? Justify. What would represent the total distance travelled (forward and backward)? c. What is the displacement over the first 6 seconds