A car travels $22.0 \mathrm{~m} / \mathrm{s}$ north for $30.0 \mathrm{~min}$ and then reverses direction and travels $28.0 \mathrm{~m} / \mathrm{s}$ for $15.0 \mathrm{~min}$. What is the car's total displacement? a) $1.44 \cdot 10^4 \mathrm{~m}$ b) $6.48 \cdot 10^4 \mathrm{~m}$ c) $3.96 \cdot 10^4 \mathrm{~m}$ d) $9.98 \cdot 10^4 \mathrm{~m}$

Find the displacement vectors from

$$P_1 to P_2,$$

where

$$P_1 and P_2$$

are the points given. Sketch

$$P_1, P_2, and \vec { P _ { 1 } P _ { 2 } }$$

$$(a) P_1(1, 0, 2), P_2(2, 1, 7)$$

$$(b) P_1(1, 6,−1), P_2(0, 4, 2)$$

$$(c) P_1(0, 4, 2), P_2(1, 6,−1)$$

$$(d) P_1(3, 1), P_2(2,−1)$$

A force $\vec{F}=(4.0 \mathrm{~N}) \hat{\mathrm{i}}+c \hat{\mathrm{j}}$ acts on a particle as the particle goes through displacement $\vec{d}=(3: 0 \mathrm{~m}) \hat{\mathrm{i}}-(2.0 \mathrm{~m}) \hat{\mathrm{i}}$ : $($ Qther forces also act on the particle.) What is $c$ if the work done on the particle by force $\vec{F}$ is 0 ?

The rigid beam is supported by a pin at $A$ and two steel wires, each having a diameter of $4 {mm}$. If the yield stress for the wires is $\sigma_Y=530 {MPa}$, and $E_{{st}}=200 {GPa}$, determine the intensity of the distributed load $w$ that can be placed on the beam and will just cause wire $E B$ to yield. What is the displacement of point $G$ for this case? Assume that the steel is elastic perfectly plastic.

The distributed loading is applied to the rigid beam, which is supported by the three bars. Each bar has a crosssectional area of $1.25 {in}^2$ and is made from a material having a stress-strain diagram that can be approximated by the two line segments. If a load of $w=25 {kip} / {ft}$ is applied to the beam, determine the stress in each bar and the vertical displacement of the beam.

Calculate $\int_C \mathbf{F}(\mathbf{r}) \cdot d \mathbf{r}$ for the following data. If F is a force, this gives the work done in the displacement along C. (Show the details.)

$$\mathbf{F}=\left[\begin{array}{lll}e^x, & e^y, & e^z\end{array}\right], \mathbf{r}=\left[\begin{array}{lll}t, & t^2, & t^2\end{array}\right]$$

from $(0,0,0)$ to (2, 4, 4). Sketch $C$.

A women has been instructed to exercise her leg for four minutes, three times per day. She tells the medical assistant that she could not do the exercises because she had to go to work. Which of the following defense mechanisms is she using?

A. Rationalization

B. Regression

C. Repression

D. Projection

E. Displacement

In Exercise, a particle moves with a velocity of $v ( t )$ $\mathrm { m } / \mathrm { s }$ along an $s$ -axis. Find the displacement and the distance traveled by the particle during the given time interval.
(a) $v ( t ) = \frac { 1 } { 2 } - 1 / r ; 1 \leq t \leq 3$ (b) $v ( t ) = 3 / \sqrt { t } ; 4 \leq t \leq 9$

In Exercise, a particle moves with acceleration $a ( t )$ $\mathrm { m } / \mathrm { s } ^ { 2 }$ along an $s$-axis and has velocity $v _ { 0 } \mathrm { m } / \mathrm { s }$ at time $t = 0 .$ Find the displacement and the distance traveled by the patticle during the given time interval.

$$a ( t ) = - 2 ; v _ { 0 } = 3 ; 1 \leq t \leq 4$$

Your patient was asked to exercise her neck for three minutes, six times a day. She told the medical assistant that she could not do the exercises because she had to go to work. Which of the following defense mechanisms is she using?

A. regression

B. rationalization

C. repression

D. projection

E. displacement

Suppose that at time $t=t_{0}$ an electron has a position vector $\mathbf{r}=2.7 \mathbf{i}-1.3 \mathbf{j}+2 \mathbf{k}$ and at a later time $t=t_{t}$ it has a position vector of $\mathbf{r}=4 \mathbf{i}-2 \mathbf{j}+\mathbf{k}$. What is the displacement of the electron during the time interval from $t_{0}$ to $t_{1}$ ?

Treatment of a 3-acylindole with $\mathrm{LiAlH}_4$ in $\left(\mathrm{CH}_3 \mathrm{CH}_2\right)_2 \mathrm{O}$ reduces the carbonyl all the way to a $\mathrm{CH}_2$ group. Explain by a plausible mechanism. (Hint: Direct $\mathrm{S}_{\mathrm{N}} 2$ displacement of alkoxide by hydride is not plausible.)

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 $a(t)=\sin t ; v_0=1 ; \pi / 4 \leq t \leq \pi / 2$ .

The velocity (in inches per second) of a particle moving along a line is

$$v(t)=\frac{2 t^2\left(t^2-1\right)}{\left(t^2+1\right)^2}$$

where $t$ is the time in seconds. Use partial fractions to find the displacement of the particle on the time interval $0 \leq t \leq 5$.