The position vector of an object moving in a plane is given by mathbfr | Mathematics I 2081

Mathematics I20815 marksNumerical: velocity speed accelerationMotion in space

The position vector of an object moving in a plane is given by $\mathbf{r}(t) = t^2 \hat{i} + t^2 \hat{j}$ . Find its velocity, speed, and acceleration when $t = 1$ and illustrate geometrically. [5]

The position vector of an object moving in a plane is given by $\mathbf{r}(t) = t^2 \hat{i} + t^2 \hat{j}$. Find its velocity, speed, and acceleration when $t = 1$ and illustrate geometrically. [5]

$\vec{r}(t) = t^2\hat{i} + t^2\hat{j}, \qquad t = 1$ --- $\vec{v}(t) = \frac{d\vec{r}}{dt} = \frac{d}{dt}(t^2)\hat{i} + \frac{d}{dt}(t^2)\hat{j} = 2t\hat{i} + 2t\hat{j}$ At $t = 1$ : $\vec{v}(1) = 2\hat{i} + 2\hat{j}$ --- $\vec{v}(t) = \sqrt{(2t)^2 + (2t)^2} = \sqrt{8t^2} = 2\sqrt{2}\,t$ A...

$$\vec{r}(t) = t^2\hat{i} + t^2\hat{j}, \qquad t = 1$$ --- $$\vec{v}(t) = \frac{d\vec{r}}{dt} = \frac{d}{dt}(t^2)\hat{i} + \frac{d}{dt}(t^2)\hat{j} = 2t\hat{i} + 2t\hat{j}$$ At $t = 1$: $$\vec{v}(1) = 2\hat{i} + 2\hat{j}$$ --- $$\vec{v}(t) = \sqrt{(2t)^2 + (2t)^2} = \sqrt{8t^2} = 2\sqrt{2},t$$ A...

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The position vector of an object moving in a plane is given by mathbfr(t) = t2 hati + t2 hatj. Find its velocity, speed, and acceleration when t = 1 and illustrate geometrically.