The position vector of the particle is given by r(t) = (2 2t)i + (1- 2t)j m.

Here's the solution to the problem.

The position vector of the particle is given by $\mathbf{r}(t) = (2\sin 2t)\mathbf{i} + (1-\cos 2t)\mathbf{j}$ m.
The mass of the particle is $m = 2 \text{ kg}$.

a) The velocity and the acceleration of the particle when $t = \frac{\pi}{6}$.

Step 1: Find the velocity vector $\mathbf{v}(t)$ by differentiating $\mathbf{r}(t)$ with respect to $t$.

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