Problem 1. (14 Points) Let y : R R be given by Y(t) = (3t – t°, 3t², 3t + t³). %3D (a) Find the velocity, the speed, and the acceleration of y. Show that y is a regular space curve. (b) Compute the unit tangent T. (c) Compute the vector y x ". (d) Compute the binormal B. (e) Compute the curvature k and the torsion T of y. Show that the curvature K and the torsion T of the curve y coincide: K(t) = T(t) for all t e R.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.