3. A particle moves in the plane so that its position is given by x(/) = / and y(1) = (f - 1)(1 + b) for OS/ $ 5. The position of the particle at r = 0 is (0.5). Assume that x and y are measured in centimeters and that ? is measured in seconds. a) Find b. b) Graph the path of the particle. The equation for x in terms of / is x(1) = 1. What is the rate of change of x with respect to r? Be sure to state the units. d) This particle is always moving to the right. How is this confirmed by the answer in 3c? e) Approximate the total distance traveled using Ar = 1 beginning at / = 0 and ending at / = 5. () Approximate the average speed of the particle over OS / $ 5 g) Write an equation for y in terms of x. h) Based on the work done in this activity, explain how to approximate the distance that a particle will travel along a curve, and also explain how to approximate the average speed of a particle over a specified time interval