Answer
(a) $r = (-3.0~\hat{i}+7.3~\hat{j})~m$
(b) $a = (-3.0~\hat{i}+8.0~\hat{j})~m/s^2$
Work Step by Step
$v(t) = (-3t~\hat{i}+2t^2~\hat{j})~m/s$
(a) $r(t) = r_0+\int_{0}^{t}~v(t)~dt$
$r(t) = r_0+\int_{0}^{t}~(-3t~\hat{i}+2t^2~\hat{j})~dt$
$r(t) = r_0+(-\frac{3}{2}t^2~\hat{i}+\frac{2}{3}t^3~\hat{j})~m$
At t = 2.0 s:
$r = (3.0~\hat{i}+2.0\hat{j})~m+(-\frac{3}{2}(2.0)^2~\hat{i}+\frac{2}{3}(2.0)^3~\hat{j})~m$
$r = (3.0~\hat{i}+2.0\hat{j})~m+(-6.0~\hat{i}+\frac{16.0}{3}~\hat{j})~m$
$r = (-3.0~\hat{i}+\frac{22.0}{3}~\hat{j})~m$
$r = (-3.0~\hat{i}+7.3~\hat{j})~m$
(b) $a(t) = \frac{dv}{dt}$
$a(t) = (-3~\hat{i}+4t~\hat{j})~m/s^2$
At t = 2.0 s:
$a = (-3.0~\hat{i}+(4.0)(2.0)~\hat{j})~m/s^2$
$a = (-3.0~\hat{i}+8.0~\hat{j})~m/s^2$
