Vector uses in physics – Calculate velocity and acceleration – Exercise 3852

Exercise

A particle moves according to the law of motion

$\vec{r}(t)=R\cos(\omega t)\vec{i}+R\sin(\omega t)\vec{j}$

Where

$\omega>0, R>0$

Calculate the velocity function, the acceleration function, their values (vector sizes) and unit vectors.

Final Answer

$\vec{v}(t)=-R\omega\sin(\omega t)\vec{i}+R\omega\cos(\omega t)\vec{j}$

$|\vec{v}(t)|=R\omega$

$\hat{v}(t)=-\sin(\omega t)\vec{i}+\cos(\omega t)\vec{j}$

$\vec{a}(t)=-R\omega^2\cos(\omega t)\vec{i}-R\omega^2\sin(\omega t)\vec{j}$

$|\vec{a}(t)|=R\omega^2$

$\hat{a}(t)=-\cos(\omega t)\vec{i}-\sin(\omega t)\vec{j}$

Coming soon…

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