The position vector of a particle is given by $\vec{r} = 3t \hat{i} + 4t^2 \hat{j}$. What is the magnitude of its velocity at $t = 1\text{ s}$?
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Question

The position vector of a particle is given by $\vec{r} = 3t \hat{i} + 4t^2 \hat{j}$. What is the magnitude of its velocity at $t = 1	ext{ s}$?

Accepted Answer

Velocity $\vec{v} = \frac{d\vec{r}}{dt} = 3\hat{i} + 8t\hat{j}$. At $t = 1	ext{ s}$, $\vec{v} = 3\hat{i} + 8\hat{j}$. Magnitude $= \sqrt{3^2 + 8^2} = \sqrt{9 + 64} = \sqrt{73}	ext{ m/s}$.

Motion in a Plane

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