A bug is traveling along a path on the coordinate plane and its position given by the equation f(t) = t sin t + 2.
a. Determine the velocity and acceleration of the bug at any time. t.
b. Write a tangent line to the path of the bug after π seconds.
c. Write a normal line to the path of the bug after π seconds.
d. What is the position of the bug when it's acceleration is π?
e. Determine the jerk of the bug at any time, t.