Question

Suppose the position of an object is given by r=(3.0t2i^6.0t3j^)m\overrightarrow{\mathbf{r}}=\left(3.0 t^2 \hat{\mathbf{i}}-6.0 t^3 \hat{\mathbf{j}}\right) \mathrm{m}. Find its velocity v\overrightarrow{\mathbf{v}} and acceleration a\overrightarrow{\mathbf{a}}, as a function of time.

Solution

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Answered 2 years ago
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Instantaneous velocity and instantaneous acceleration are given by

v=drdt\displaystyle \vec{\mathrm{v}}=\frac{d\vec{\mathrm{r}}}{dt} \ \ \ \ \ (3-8) and

a=dvdt\vec{\mathrm{a}}= \displaystyle \frac{d\vec{\mathrm{v}}}{dt} \ \ \ \ \ (3-11)

(a)(a)

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