An introductory exploration of parametric equations.

Slide time slider.
1. Describe the motion. Do the two points start out at the same location? Which point is furthest from the origin when the time is 10? If this was a race, is there ever a time between 0 and 10 that team diamond and team circle are neck and neck? If so, how many times? If you knew the equation for x(t), how could you find out when and where they were at the same location?
2. a. When the time is 3.5, which point is moving faster?
b. When the time is 8, which point is moving faster?
3. The parametric equations are defined as follows:
x1(t) = 0.05t^3 – 0.2t^2 – 0.5t – 5 and x2(t) = t – 7sin(t)
Which equation models the movement of the square and which models the diamond? Find the velocity of each at t = 3.5 and t = 8. Show your work. Give your answers to three decimal places.
4. Find the acceleration for both objects at t = 3.5 and t = 8.
5. Using calculus terms, explain what the sign of the answers in Exercises 3 and 4 implies for the motion.