A particle moves with acceleration a(t) m/

$$s^2$$

along and s-axis and has velocity

$$v_0$$

m/s at time t=0. FInd the displacement and the distance traveled by the particle during the given time interval. a(t)=-2;

$$v_0$$

=3;

$$1 \leq t \leq 4$$

A particle moves with acceleration a(t) along an s-axis and has velocity $v_0 \mathrm{~m} / \mathrm{s}$ at time t=0. Determine the displacement and the distance traveled by the particle during the given time interval for $a(t)=3 ; v_0=-1 ; 0 \leq t \leq 2$ .

Calculate ∫_C F(r)*dx for the given data. If F is a force, this gives the work done by the force in the displacement along C. Show the details. F=[x.-z.2y] from (0, 0, 0) straight to (1, 1, 0), then to (1, 1, 1), back to (0, 0, 0)

Solve the given problems.

The displacement $y$ (in $\mathrm{cm}$ ) of an object at the end of a spring is described by the equation $d^2 y / d t^2+4 d y / d t+4 y=0$, where $t$ is the time (in s). Find $y=f(t)$ if $f(0)=0$ and $f(1)=0.50 \mathrm{~cm}$.

A particle moves with acceleration a(t) along an s-axis and has velocity $v_0 \mathrm{~m} / \mathrm{s}$ at time t=0. Determine the displacement and the distance traveled by the particle during the given time interval for $a(t)=t-2 ; v_0=0 ; 1 \leq t \leq 5$.

A sinusoidal transverse wave of wavelength 20 cm travels along a string in the positive direction of an x axis. The displacement y of the string particle at x=0 is given in the figure as a function of time $t$. The wave equation is to be in the form of $y(x, t)=$ $y_m \sin (k x \pm \omega t+\phi)$. What are the sign in front of $\omega$

Use the d'Alembert solution $u(x, t)=F(x+c t)+G(x-c t)$ to find the displacement u(x, t) of the string of length L with fixed endpoints, initial displacement u(x, 0)=f(x), and initial velocity $u_{t}(x, 0)=0$. Sketch the solution as a function of x, $0 \leq x \leq L$, for the specific values of t that are given. c=1, L=10, and

$$f(x)=\left\{\begin{array}{ll} 0, & \mathrm { for } \ 0 \leq x \leq 5, \\ x-5, & \mathrm { for } \ 5<x \leq 6, \\ 7-x, & \mathrm { for } \ 6<x \leq 7, \\ 0, & \mathrm { for } \ 7<x \leq 10 \end{array}\right.$$

Plot u(x, t) as a function of x for t=2, 4, 6, 8, 10, 12.

A particle moves with acceleration a(t) m/s² along an s-axis and has velocity

$$v_0$$

m/s at time t=0. FInd the displacement and the distance traveled by the particle during the given time interval. a(t)=sin t;

$$v_0=1$$

; π/4≤t≤π/2

The velocity of a particle moving along the $x$-axis is given, for $t>0$, by $v_x=\left(50.0 t-2.0 t^3\right) \mathrm{m} / \mathrm{s}$, where $t$ is in seconds. What is the acceleration of the particle when (after $t=0$ ) it achieves its maximum displacement in the positive $x$-direction?

Write the ratio as a fraction in simplest form. 15. 16 dogs to 12 cats

Square ABCD has vertices at (0, 0), (0, 2), (2, 2), and (2, 0). Perform the indicated transformation. Then give the coordinates of figure

$$A ^ { \prime } B ^ { \prime } C ^ { \prime } D ^ { \prime }$$

.

$$( x , y ) \rightarrow ( x + 3 , y )$$

Given

$$A=\left[\begin{array}{rrr} 5 & 0 & 1 \\ -2 & 3 & 7 \\ 0 & -6 & 2 \end{array}\right]$$

Determinethe following minors and cofactors of $A$.

(a) $M_{13}$ and $C_{13}$ (b) $M_{22}$ and $C_{22}$ (c) $M_{31}$ and $C_{31}$ (d) $M_{33}$ and $C_{33}$

Perform the indicated calculation.

$$_ { 8 } P _ { 6 }$$

(a) Prove that there exist unique scalars $c_0,c_1,\dots,c_n$ such that

$$f(-1)+f(-2)=c_0f(0)+c_1f(1)+\dots+c_nf(n)$$

for every polynomial $f(x)$ in $\mathcal{P}_n$. (b) Find the scalars $c_0,c_1,c_2,c_3,$ and $c_4$ such that

$$f(-1)+f(-2)=c_0f(0)+c_1f(1)+c_2f(2)+c_3f(3)+c_4f(4)$$

for every polynomial $f(x)$ in $\mathcal{P}_4$.