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(B) The position vector of the particle is given by $\vec{r}(t) = (3t)\hat{i} + (4t^2)\hat{j}$.To find the velocity vector $\vec{v}(t)$,we differentia

Vedclass · Accepted Answer

$3\hat{i} + 16\hat{j}$

Vedclass · Answer

(B) The position vector of the particle is given by $\vec{r}(t) = (3t)\hat{i} + (4t^2)\hat{j}$.To find the velocity vector $\vec{v}(t)$,we differentiate the position vector with respect to time $t$:$\vec{v}(t) = \frac{d\vec{r}}{dt} = \frac{d}{dt} [(3t)\hat{i} + (4t^2)\hat{j}]$$\vec{v}(t) = 3\hat{i} + (8t)\hat{j}$.Now,substitute $t = 2 \ s$ into the velocity equation:$\vec{v}(2) = 3\hat{i} + (8 	imes 2)\hat{j}$$\vec{v}(2) = 3\hat{i} + 16\hat{j} \ m/s$.

If the position vector of a particle is given by $\vec{r}(t) = (3t)\hat{i} + (4t^2)\hat{j}$,then obtain its velocity vector at $t = 2 \ s$.

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