Chapter 11.4, Problem 11.94P

A girl operates a radio-controlled model car in a vacant parking lot. The girl's position is at the origin of the xy coordinate axes, and the surface of the parking lot lies in the x-y plane. The motion of the car is defined by the position vector $\text{r}=\left(2+2t^2\right)\text{i}+\left(6+t^3\right)\text{j}$ , where r and t are expressed in meters and seconds, respectively. Determine (a) the distance between the car and the girl when $t=2$ s, (b) the distance the car traveled in the interval from $t=0$ to $t=2$ s, (c) the speed and direction of the car's velocity at $t=2$ s, (d) the magnitude of the car's acceleration at $t=2$ s.