4. 2D Kinematics

The position of a squirrel running in a park is given by $\(\vec{r}\) = \(\left\)[ (0.280~\(\mathrm{m/s}\))t + (0.0360~\(\mathrm{m/s^2}\))t^2 \(\right\)] \(\hat{i}\) + (0.0190~\(\mathrm{m/s^3}\))t^3 \(\hat{j}\)$. (a) What are $v_x\left(t\right)$ and $v_y\left(t\right)$, the $x$-and $y$-components of the velocity of the squirrel, as functions of time?

Two athletes start from the same point. One runs east at $10$ mph, and the other runs south at $10$ mph. After $1$ hour, what is the magnitude of the displacement between them?

If you ride your bicycle a distance of $40 m$ and the front wheel has a diameter of $0.8 m$, how many complete revolutions does the front wheel make?

A frog's tongue moves at a constant speed of $2 m/s$. During a total time of $50 \mathrm{ms}$ (which is $\frac{1}{20}$ of a second), how far does the tongue reach?

A particle moves in the xy-plane such that its position as a function of time is given by $x=3t$ and $y=4\sin \left(\pi t\right)$, where $t$ is in seconds. A string is attached from the origin to the particle. At certain times, the string will be perfectly straight (i.e., the particle passes through the x-axis). Find the first time $t_1$ with $t_1>0$ when this is true.

A particle moves along a path such that its position in polar coordinates is given by $r=2\cos \left(t\right)$ ft and $\theta =\frac{t}{2}$ rad, where $t$ is in seconds. What is the displacement vector of the particle from $t=0$ to $t=2$ seconds?

In which situation is position best described using two dimensions?

Three particles are fixed on an $x$ axis at positions $x=2m$, $x=5m$, and $x=9m$. What is the displacement of a particle that moves from the first to the third position?

How can the position of a very tiny particle in two-dimensional motion be determined?

In the context of simulating or showing motion in an assembly, why must at least $1$ degree of freedom be maintained?

Which of the following best describes the direction of the vector field $f(x,y)$ where $f(x,y)=\frac{yi-xj}{x^2+y^2}$?

In a two-dimensional tug of war, two teams pull on a rope with forces represented by vectors $F_1$ and $F_2$. What does the net force on the rope equal?

A web page designer creates an animation in which a dot on a computer screen has position $\overrightarrow{r}=[4.0\mathrm{cm}+\left(2.5{\text{ cm/s}}^2\right)t^2]i+\left(5.0\mathrm{cm/s}\right)tj$. Find the magnitude and direction of the dot's average velocity between $t=0$ and $t=2.0s$.

A thin semicircular rod of radius $R$ lies in the $xy$-plane with its ends at $(R,0)$ and $(-R,0)$. What are the coordinates of the center of mass of the rod?

Which of the following types of motion requires acceleration in more than one plane ($\mathrm{multiplanar}\mathrm{acceleration}$)?