VELOCITY-ACCELERATION

  1. A particle moves along the so that its velocity at any time is given by.The position is 5 for.
  2. Write a polynomial expression for the position of the particle at any time.
  3. For what values of,, is the particle’s instantaneous velocity the same as its average velocity on the closed interval?
  4. Find the total distance traveled by the particle from time until.
  1. A particle moves along the with velocity given by for .
  2. In which direction (up or down) is the particle moving at time ? Why?
  3. Find the acceleration of the particle at time . Is the velocity of the particle increasing at ? Why or why not?
  4. Given that is the position of the particle at time and that , find .
  5. Find the total distance traveled by the particle from until .

t (seconds) / v(t) (feet per sec)
0 / 0
5 / 12
10 / 20
15 / 30
20 / 55
25 / 70
30 / 78
35 / 81
40 / 75
45 / 60
50 / 72

  1. The graph of velocity , in of a car traveling on a straight road for , is shown above. A table of values for , at 5 second intervals of time is shown to the right of the graph.
  2. During what time intervals is the acceleration of the car positive?
  3. Find the average acceleration of the car in over the interval .
  4. Find one approximation for the acceleration of the car in at . Show the computations used to arrive at your answer.
  5. Approximate with a Riemann sum, using the midpoints of the five subintervals of equal length. Using correct units, explain the meaning ofthis integral.

  1. Two runners, A and B, run on a straight racetrack for seconds. The graph above, which consists of two line segments, shows the velocity, in meters per second, of Runner A. The velocity, in meters per second, of Runner B is given by .
  2. Find the velocity of Runner A and the velocity of Runner B at time seconds. Indicate units of measure.
  3. Find the acceleration of Runner A and the acceleration of Runner B at time seconds. Indicate units of measure.
  4. Find the total distance run by Runner A and the total distance run by Runner B over the interval seconds. Indicate units of measure.
  5. A car is traveling on a straight road with velocity 55 at time . For seconds, the cars acceleration, in , is the piecewise linear function defined by the graph above.
  6. Is the velocity of the car increasing at seconds? Why or why not?
  7. At what time in the interval seconds, other than , is the velocity of the car 55 ? Why?
  8. On the time interval seconds, what is the car’s absolute maximum velocity, in , and at what time does it occur? Justify your answer.
  9. At what time in the interval seconds, if any, is the car’s velocity equal to zero? Justify your answer.