Find the velocity, acceleration, and speed of a particle with the given position function. r ( t ) = e^ t ( cos t i + sin t j + t k )

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Uttam SaikiaLv10

14 Dec 2020

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To find the velocity and acceleration vectors for uniform circularmotion and to recognize that this acceleration is the centripetalacceleration.
Suppose that a particle's position is given by the followingexpression:

\vec{r}(t)= R[\cos(\omega t)\hat{i} + \sin(\omega t)\hat{j}]
\,\ \qquad = R\cos(\omega t)\hat{i} + R\sin(\omega t)\hat{j}.

a) When does the particle first cross the negative x axis?
b)Find the particle's velocity as a function of time.
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d)Now find the acceleration of the particle.
e)Your calculation is actually a derivation of the centripetalacceleration. To see this, express the acceleration of the particlein terms of its position r_vec(t).

Find the velocity, acceleration, and speed of a particle with position function

r(t)=〈2tsint, 2tcost, −2t^2〉

v(t) = <___,___,___>

a(t) = <___,___,___>

|v(t)| = <___>