Mathematics: Aparticle is moving with the given data. find the position of the particle. a(t)=10sin(t)+3cos(t) s(0)=0 s(2pi)=12

Aparticle is moving with the given data. find the

Ответ:

rvj0444073603

02.01.2022

$a(t)=10\sin t+3\cos t$

$v(t)=\displaystyle\int a(t)\,\mathrm dt$
$v(t)=\displaystyle\int(10\sin t+3\cos t)\,\mathrm dt$
$v(t)=-10\cos t+3\sin t+C_1$

$s(t)=\displaystyle\int v(t)\,\mathrm dt$
$s(t)=\displaystyle\int(-10\cos t+3\sin t+C_1)\,\mathrm dt$
$s(t)=-10\sin t-3\cos t+C_1t+C_2$

With the boundary conditions s(0)=0

and $s(2\pi)=12$ , we have

$\begin{cases}0=-3+C_2&s(0)=0\\12=-3+2\pi C_1+C_2&s(2\pi)=12\end{cases}\implies C_1=\dfrac6\pi,C_2=3$

so that the position of the particle is given by

$s(t)=-10\sin t-3\cos t+\dfrac{6t}\pi+3$

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Ответ:

boomerjm

29.10.2020

Mathematics

D. She can use the commutative property to rewrite the expression as (70 + 30 + 12.8) + 6.1

Step-by-step explanation:

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Aparticle is moving with the given data. find the position of the particle. a(t)=10sin(t)+3cos(t) s(0)=0 s(2pi)=12

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