Question

A particle moves along ay-plane with a position ofx (t) = sin(2t) + 3 cos(4t)y (t) = sin(t) – 6 cos(3t)a. Determine the position vector of the particle.b. Determine the velocity vector of the particle.c. Determine the acceleration vector of the particle.d. Determine the position vector of the particle when t = 4s.e. Determine the average acceleration from t = 0s to t= 5s.f. Determine the instantaneous acceleration when të Is.g. Determine the average velocity from t = ls to t= 3s.​

Answer 1

a)

$$\vec{r}=\begin{pmatrix} \sin(2t) + 3 \cos(4t) \\ \sin(t) – 6 \cos(3t) \end{pmatrix}$$

b)

$$\vec{v}=\begin{pmatrix} 2 \cos(2t) -12\sin(4t) \\ \cos(t) +18 \sin(3t) \end{pmatrix}$$

c)

$$\vec{a}=\begin{pmatrix} -4 \sin(2t) -48\cos(4t) \\ - \sin(t) +54 \cos(3t) \end{pmatrix}$$

d)

$$\vec{r}=\begin{pmatrix} -1.88 \\ - 5.82 \end{pmatrix}$$

e)

$$\vec{a}_{av}=\begin{pmatrix} -2.93 \\ 2.20 \end{pmatrix}$$

f)

$$\vec{a}(5)=\begin{pmatrix} -17.4\\ -40.1 \end{pmatrix}$$

g)

$$\vec{v}_{av}=\begin{pmatrix} 1.65 \\ -0.59 \end{pmatrix}$$