Answer
(a) Suppose the motion of the particle over the time period is modeled by the equation $r(t)$: the velocity of the particle along the curve is $v(t)=r'(t)$; the speed of the particle is $|v(t)|=|r'(t)|$; the acceleration is $a(t)=v'(t)=r''(t)$
(b) If the position of the particle is given by $r(t)$, then
$a_T=\dfrac{r'(t) \cdot r''(t)}{|r'(t)|}$
and
$a_N=\dfrac{r'(t) \times r''(t)}{|r'(t)|}$
Work Step by Step
(a) Suppose the motion of the particle over the time period is modeled by the equation $r(t)$: the velocity of the particle along the curve is $v(t)=r'(t)$; the speed of the particle is $|v(t)|=|r'(t)|$; the acceleration is $a(t)=v'(t)=r''(t)$
(b) If the position of the particle is given by $r(t)$, then
$a_T=\dfrac{r'(t) \cdot r''(t)}{|r'(t)|}$
and
$a_N=\dfrac{r'(t) \times r''(t)}{|r'(t)|}$
