The position vector for a particle is given as a function of time by \(\vec{r} = x(t)\hat{i} + y(t)\hat{j}\),
with \(x(t) = at + b\) and \(y(t) = ct^2 + d\), where \(a = 1.99\) (m/s), \(b = 1\) (m), \(c = 0.28\)
(m/s^2), and \(d = 2.1\) (m). Determine the following quantities at \(t = 2.21\) (s):
Note: give your answer as a number with 3 significant figures (without units). Use dot (.)
for decimal point.
(a) the distance from the particle to the origin O(0,0) of the coordinate system (m)
(b) the speed of the particle (m/s)
(c) the magnitude of the acceleration (m/s^2)