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selesaikan persoalan tersebut dengan rinci

The problem involves the motion of a particle described by the parametric function \( f(t) = (3 \cos t, \sin t) \), where \( t \in [0, 2\pi] \).

Let's break down and solve each part step by step:

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### (a) Sketch the curve of the particle's path
The given parametric equation is:

\[
f(t) = (x(t), y(t)) = (3 \cos t, \sin t), \quad t \in [0, 2\pi]
\]

- The \( x(t) = 3 \cos t \) suggests an oscillation in the horizontal direction with an amplitude of 3.
- The \( y(t) = \sin t \) suggests a standard sinusoidal wave in

Misalkan suatu partikel bergerak yang posisinya setiap saat t diberikan oleh fungsi lintasan berikut f(t) = (3 cos t, sin t), t ∈ [0, 2π].

(a) Buatlah sketsa kurva lintasan partikel
(b) Tentukan kecepatan dan laju partikel pada saat t = π/4
(c) Tentukan percepatan partikel di setiap saat t
(d) Tentukan panjang lintasan yang ditempuh partikel dari t = 0 sampai dengan t = π/4

Explore the detailed solution of a parametric motion problem where a particle's path is given by f(t) = (3 cos t, sin t) for t ∈ [0, 2π]. Includes finding velocity, acceleration, and the arc length traveled by the particle at specified times.

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