Answer
a) See the explanation.
b) See the explanation.
Work Step by Step
a)
Let us say that $r(t)$ denotes the position vector of the particle on the space curve $C$.
The velocity vector is calculated as: $v(t)=r'(t)$
The speed of the particle is calculated as: $|v(t)|$ or, $|r'(t)|$
The acceleration of the particle is calculated as: $a(t)=v'(t)=r''(t)$
b)
Acceleration in terms of its tangential components $T$ and normal components $N$ is calculated as:
$a=a_TT+a_NN$
Here, $a_T$ denotes $v'(t)$ and $a_N$ denotes $ \kappa v^2$.
