Let aT be the tangential component of the acceleration?

Question

Let aT be the tangential component of the acceleration vector of r(t)=<t-sin(t), 1-cos(t), 0>. What is (aT)^2 at t=pi/2?

r'(t)=<1-cos(t), sin(t), 0>

r''(t)=<sin(t), cos(t), 0>

r'(pi/2)=<1, 1, 0>

r''(pi/2)=<1, 0, 0>

Then what should I do?

Answer 1

a_T^2 = |r''(pi/2)|^2 = 1^2+0^2+0^2 = 1