An object, which is at the origin at time $t=0$, has initial velocity $\overrightarrow{\mathbf{v}}_0=(-14.0 \hat{\mathbf{i}}-7.0 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}$ and constant acceleration $\overrightarrow{\mathbf{a}}=(6.0 \hat{\mathbf{i}}+3.0 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}^2$. Determine the position $\overrightarrow{\mathbf{r}}$ where the object comes to rest (momentarily).

Suppose the position of an object is given by $\overrightarrow{\mathbf{r}}=\left(3.0 t^2 \hat{\mathbf{i}}-6.0 t^3 \hat{\mathbf{j}}\right) \mathrm{m}$. Find its velocity $\overrightarrow{\mathbf{v}}$ and acceleration $\overrightarrow{\mathbf{a}}$, as a function of time.

A hiker follows a winding trail for $5.5$ hours while climbing a mountain. The distance along the trail is $11.5 \mathrm{~km}$ and the summit is $850 \mathrm{~m}$ above and $8.0 \mathrm{~km}$ due north of the starting point. What are the average speed and the magnitude and direction of the average velocity vector?

At $t=0$, a particle starts from rest at $x=0, y=0$, and moves in the $x y$ plane with an acceleration $\overrightarrow{\mathbf{a}}=(4.0 \hat{\mathbf{i}}+3.0 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}^2$. Find the speed of the particle.

At $t=0$, a particle starts from rest at $x=0, y=0$, and moves in the $x y$ plane with an acceleration $\overrightarrow{\mathbf{a}}=(4.0 \hat{\mathbf{i}}+3.0 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}^2$. Find the $x$ and $y$ components of velocity.

What was the average velocity of the particle in Problem 19 between $t=1.00 \mathrm{~s}$ and $t=3.00 \mathrm{~s}$ ? What is the magnitude of the instantaneous velocity at $t=2.00 \mathrm{~s}$ ?

You are given a vector in the $x y$ plane that has a magnitude of $95.0$ units and a $y$ component of $-60.0$ units.

Assuming the $x$ component is known to be positive, specify the vector which, if you add it to the original one, would give a resultant vector that is $80.0$ units long and points entirely in the $-x$ direction.

You are given a vector in the $x y$ plane that has a magnitude of $95.0$ units and a $y$ component of $-60.0$ units. What are the two possibilities for its $x$ component?

Suppose a vector $\overrightarrow{\mathbf{V}}$ makes an angle $\phi$ with respect to the $y$ axis. What could be the $x$ and $y$ components of the vector $\overrightarrow{\mathbf{V}}$ ?

Let $\overrightarrow{\mathbf{V}}_1=-6.0 \hat{\mathbf{i}}+8.0 \hat{\mathbf{j}}$ and $\overrightarrow{\mathbf{V}}_2=-4.5 \hat{\mathbf{i}}-5.0 \hat{\mathbf{j}}$ find the magnitude and direction of $\overrightarrow{\mathbf{V}}_1-\overrightarrow{\mathbf{V}}_2$.

Let $\overrightarrow{\mathbf{V}}_1=-6.0 \hat{\mathbf{i}}+8.0 \hat{\mathbf{j}}$ and $\overrightarrow{\mathbf{V}}_2=4.5 \hat{\mathbf{i}}-5.0 \hat{\mathbf{j}}$. Find the magnitude and direction of $\overrightarrow{\mathbf{V}}_2-\overrightarrow{\mathbf{V}}_1$.

Let $\overrightarrow{\mathbf{V}}_1=-6.0 \hat{\mathbf{i}}+8.0 \hat{\mathbf{j}}$ and $\overrightarrow{\mathbf{V}}_2=-4.5 \hat{\mathbf{i}}-5.0 \hat{\mathbf{j}}$ Find the magnitude and direction of $\overrightarrow{\mathbf{V}}_1+\overrightarrow{\mathbf{V}}_2$.

You dive straight down into a pool of water. You hit the water with a speed of $5.0 \mathrm{~m} / \mathrm{~s}$, and your mass is $75 \mathrm{~kg}$. Assuming a drag force of the form $F_{\mathrm{~D}}=-\left(1.00 \times 10^4 \mathrm{~kg} / \mathrm{~s}\right) v$, how long does it take you to reach $2 \%$ of your original speed? (Ignore any effects of buoyancy.)

Let $\overrightarrow{\mathbf{V}}_1=-6.0 \hat{\mathbf{i}}+8.0 \hat{\mathbf{j}}$ and $\overrightarrow{\mathbf{V}}_2=-4.5 \hat{\mathbf{i}}-5.0 \hat{\mathbf{j}}$ Find the magnitude and direction of $\overrightarrow{\mathbf{V}}_2$.