Vector uses in physics – Calculate velocity and acceleration – Exercise 3862

Exercise

A point moves along the curve

$\vec{r}(t)=2\cos t\vec{i}+3\sin t\vec{j}+4t\vec{k}$

Calculate the velocity and acceleration of the point in time

$t=\frac{\pi}{2}$

Final Answer

$\vec{v}(t)=-2\sin t\vec{i}+3\cos t\vec{j}+4\vec{k}$

$\vec{v}(\frac{\pi}{2})=-2\vec{i}+4\vec{k}$

$\vec{a}(t)=-2\cos t\vec{i}-3\sin t\vec{j}+0\vec{k}$

$\vec{a}(\frac{\pi}{2})=-3\vec{j}$

Coming soon…

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