A particle P has position vector r_P = \(t2+1)i + (3t-2)j at time t seconds. Find the position vector of P at t=3s.

Here are the solutions to the problems:

Question 1:
The position vector of particle P at $t$ seconds is given by $\mathbf{r}_P = \{(t^2+1)\mathbf{i} + (3t-2)\mathbf{j}\}m$.

*a) Find the position vector of P at $t=3$.
Substitute $t=3$ into the position vector equation:

$$\mathbf{r}_P(3) = ((3)^2+1)\mathbf{i} + (3(3)-2)\mathbf{j}$$ $$\mathbf{r}_P(3) = (9+1)\mathbf{i} + (9-2)\mathbf{j}$$ $$$$