4. 2D Kinematics

A race car moves along a circular track of radius $R$. If the car is located at a point on the track that is directly east of the center, how many radius lengths east of the track's center is the car's position?

A wheel rolls without slipping on a horizontal surface. At a given instant, which of the following best represents the velocity vector of point $P$ located at the top of the wheel relative to the ground?

A solid sphere of radius $R$ rolls without slipping along the x-axis. If its center moves from position $(x,y)$ = $(0,R)$ to $(4R,R)$, what is the magnitude of the displacement of the point on the sphere that was initially at the bottom (touching the ground)?

Which of the following diagrams correctly shows the direction of wind motion between a region of high atmospheric pressure ($P^{high}$) and a region of low atmospheric pressure ($P^{low}$) (neglecting the Coriolis effect)?

A particle leaves the origin with an initial velocity of $3m/s$ in the x-direction and $4m/s$ in the y-direction. What is the magnitude of its initial velocity?

A boat is traveling east across a river with a velocity of $5m/s$ relative to the water. The river flows north at $3m/s$. What is the magnitude of the boat's velocity relative to the ground?

An object starts at position $x=0m$ and travels with a constant velocity of $v=3\frac{m}{s}$ along the x-axis. What is its position after $4s$?

Graphically determine the resultant of the following three vector displacements: 26 m, 33° west of south.

Which of the following is a simple model commonly used to help understand the forces acting on an object in two-dimensional motion?

Ignoring friction and air resistance, if you start from rest and accelerate at a constant rate of $2m/s^2$, how fast will you be moving after $10s$?

You have a remote-controlled car that has been programmed to have velocity $v=(-3ti+2t^{2}j)\text{m/s}$, where t is in s. At t = 0 s, the car is at $r_0=(3.0i+2.0j)\text{m}$. What are the car's position vector?

In a two-dimensional pulley system, a block moves horizontally to the right by $3m$ and then vertically upward by $4m$. What is the magnitude of the block's total displacement?

A wheel starts from rest and rotates with a constant angular acceleration until it comes to a stop after reaching an angular velocity of $\omega =0$ at time $t$. If its initial angular velocity was $\omega ={\omega }_0$ at $t=0$, through what total angle $\theta$ did the wheel turn between $t=0$ and the time it stopped?

At point A, a hiker is 10m east from the origin. After 35s, the hiker arrives at point B 40m at 60° north of east from the origin. Calculate the magnitude and direction of the hiker's displacement.