Chapter 12.3, Problem 9E

Finding Velocity and Acceleration Along a Plane Curve In Exercises 3-10, the position vector r describes the path of an object moving in the x y-plane.

(a) Find the velocity vector, speed, and acceleration vector of the object.

(b) Evaluate the velocity vector and acceleration vector of the object at the given point.

(c) Sketch a graph of the path and sketch the velocity and acceleration vectors at the given point.

Position Vector Point

$r(t)=\langle t-\sin t,1-\cos t\rangle$ $(\pi ,2)$