A particle P has a position vector given by r_P = (t2 + 1)i + (3t − 2)j m. Find the position vector of P at t=3 s.

Here are the solutions to your problems, step-by-step:

1. Position and Velocity Vectors
Given: Position vector of particle P: $\mathbf{r}_P = (t^2 + 1)\mathbf{i} + (3t - 2)\mathbf{j}$ m.

a) Find the position vector of P at $t=3$ s.

Step 1: Substitute $t=3$ into the position vector equation.

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