Question: If \(x\left( t \right)=\left( t,\sin 4t,\cos 4t \right),\,\,0\le t\le \pi \), find

(a) The velocity, speed and acceleration at any time

(b) The length of the arc of the curve

(c) A parametrization of the curve by arc length

(d) \(T,N\) and \(\kappa \) at \(t=\frac{\pi }{2}\)

(e) The tangential and normal components of acceleration