Question

1. A plane curve has been parametrized with the following vector-valued function, r(t) = (t + 2)i + (-2t2 + t + 1)j a. Carefully make 2 sketches of the plane curve over the interval . (5 pts) b. Compute the velocity and acceleration vectors, v(t) and a(t). (6 pts) c. On the 1st graph, sketch the position, velocity and acceleration vectors at t=-1. (5 pts) d. Compute the unit tangent and principal unit normal vectors, T and N at t=-1. (6 pts) e. Compute the curvature, κ(t), at t=-1 using 3 different methods. (12 pts) f. Compute the normal and tangential components of the acceleration vector, and , at t=-1. Also verify the value of using an alternative method. (9 pts) g. On the 2nd graph, again sketch the acceleration vector at t=-1 as well as sketch the normal and tangential vector components of the acceleration vector, and . (6 pts)

Answer 1