Find the tangential and normal components of the acceleratio

Find the tangential and normal components of the acceleration vector of a particle with position function (t) = t + 2t + t2 .

Solution

r(t) = ti + 2tj +t²k

r\' (t) = i + 2j + 2tk

r\'\' (t) = 2k

acceleration = r\'\' (t) , therefore there is no tangential component of the acceleration, and 2k in the normal component