Chapter 12.2, Problem 19E

(a)

To determine

To calculate: The first derivative of the function $r\left(t\right)=t^{3}i+\frac{1}{2}{t}^{2}j$.

(b)

To determine

To calculate: The second derivative of the function $r\left(t\right)=t^{3}i+\frac{1}{2}{t}^{2}j$.

(c)

To determine

To calculate: The dot product of the first derivative and second derivative of the function $r\left(t\right)=t^{3}i+\frac{1}{2}{t}^{2}j$.