A baseball is flying in R 3 along the curve parametrized by

A baseball is flying in R 3 along the curve parametrized by x(t) = t, 2t 3 3 , t2 where t denotes time. (a) Find the speed of the baseball as a function of time. (Hint: For all parts of this problem, the answers are fairly nice — you should not have to do a lot of tedious calculations.) (b) How far does the baseball travel between times t = 0 and t = 3? (c) Find the curvature of the baseball’s trajectory as a function of t. (d) Find the torsion as a function of t.

Solution

A baseball is flying in R 3 along the curve parametrized by x(t) = t, 2t 3 3 , t2 where t denotes time. (a) Find the speed of the baseball as a function of time.