Position vector of a particle is given as
`r = 2t hati +3t^(2) hatj` where t is in second and the coefficients have the proper units, for r to be in metres.
(i) Find instantaneous velocity v(t) of the particle.
(ii) Find magnitude and direction of v(t) at `t = 2s`

Explanation

To solve the problem step by step, we will follow the instructions given in the question regarding the position vector of the particle.

### Given:
The position vector of the particle is:
\[ \mathbf{r}(t) = 2t \hat{i} + 3t^2 \hat{j} \]

### (i) Find the instantaneous velocity \( \mathbf{v}(t) \) of the particle.

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