(Solved): Ameena ride a roller-coaster during her visit to the Genting Highland theme park. The rollercoa ...

Ameena ride a roller-coaster during her visit to the Genting Highland theme park. The rollercoaster moves with an acceleration $$\mathbf{a}(t)=e^{2t+1}\mathbf{i}+\left(1?2t^3\right)\mathbf{k}$$, where $$t$$ is measured in second and the vector components measured in meter. Find her position at $$t=0.05$$ minutes given the initial condition $$\mathbf{v}(0)=\mathbf{i}+\mathbf{j}+2\mathbf{k}$$ and $$\mathbf{r}(0)=\frac{1}{2}{e}^1\mathbf{i}+10\mathbf{j}$$