The vector position of a particle varies in time according to the expression $\overrightarrow{\mathbf{r}}=3.00 \hat{\mathbf{i}}-6.00 t^{2} \hat{\mathbf{j}},$ where $\overrightarrow{\mathbf{r}}$ is in meters and t is in seconds. (a) Find an expression for the velocity of the particle as a function of time. (b) Determine the acceleration of the particle as a function of time. (c) Calculate the particle's position and velocity at t = 1.00 s.

The position of a particle moving along the $x$-axis varies with time according to $x(t)=5.0 t^2-4.0 t^3 \mathrm{~m}$. Find (a) the velocity and acceleration of the particle as functions of time, (b) the velocity and acceleration at $t=2.0 \mathrm{~s}$, (c) the time at which the position is a maximum, (d) the time at which the velocity is zero, and (e) the maximum position.

The vector position of a particle varies in time according to the expression $\mathbf{r}=\left(3.00 \hat{\mathbf{i}}-6.00 t^2 \hat{\mathbf{j}}\right) \mathrm{m}$. (a) Find expres sions for the velocity and acceleration as functions of time.

A river has a steady speed of 0.500 m/s. A student swims upstream a distance of 1.00 km and swims back to the starting point. (a) If the student can swim at a speed of 1.20 m/s in still water, how long does the trip take? (b) How much time is required in still water for the same length swim? (c) Intuitively, why does the swim take longer when there is a current?

A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of $8.00 \mathrm{~m} / \mathrm{s}$ at an angle of $20.0^{\circ}$ below the horizontal. It strikes the ground $3.00 \mathrm{~s}$ later. How long does it take the ball to reach a point $10.0 \mathrm{~m}$ below the level of launching?

A river has a steady speed of 0.500 m/s. A student swims upstream a distance of 1.00 km and swims back to the starting point. Intuitively, why does the swim take longer when there is a current?

A particle initially located at the origin has an acceleration of $\overrightarrow{\mathbf{a}}=3.00 \hat{\mathbf{j}}\ \mathrm{m} / \mathrm{s}^{2}$ and an initial velocity of $\overrightarrow{\mathbf{v}}_{i}=5.00 \hat{\mathbf{i}}\ \mathrm{m} / \mathrm{s} .$ Find (a) the vector position of the particle at any time t, (b) the velocity of the particle at any time t, (c) the coordinates of the particle at t = 2.00 s and (d) the speed of the particle at t = 2.00 s.

Air “breaks down” when the electric field strength reaches $3.0 \times 10^{6} \mathrm{N} / \mathrm{C}$, causing a spark. A parallel-plate capacitor is made from two $4.0 \mathrm{cm} \times 4.0 \mathrm{cm}$ electrodes. How many electrons must be transferred from one electrode to the other to create a spark between the electrodes?

You witnessed a bank robbery last night! Look at the pictures below that illustrate what happened, then write complete sentences to answer the police officer's questions that follow. Use the preterite forms of the verbs ser and/or ir in each sentence. ¿Adónde fuiste tú? _____

You are working for a company that creates special magnetic environments. Your new supervisor has come from the financial side of the organization rather than the technical side. He has promised a client that the company can provide a device that will create a magnetic field inside a cylindrical chamber that is directed along the cylinder axis at all points in the chamber and increases in the axial direction as the square of the value of y, where y is the in the axial direction and y = 0 is at the bottom end of the cylinder. Prepare a calculation to show that the field requested by your supervisor and promised to a client is impossible.

Rewrite the expression with positive exponents and simplify. $8 \cdot(-2)^{-2} \cdot 4^{-1}$

Find the indicated derivative. $\frac{d z}{d x}$ if $z=e^{7}-2 e x^{7}$

Heather in her Corvette accelerates at the rate of $(3.00 \hat{\mathbf{i}}-2.00 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}^2$, while Jill in her Jaguar accelerates at $(1.00 \hat{\mathbf{i}}+3.00 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}^2$. They both start from rest at the origin of an $x y$ coordinate system. After $5.00 \mathrm{~s}$, (a) what is Heather's speed with respect to Jill, (b) how far apart are they, and (c) what is Heather's acceleration relative to Jill?

Vector $\vec { A }$ is 3.00 units in length and points along the positive x-axis. Vector $\vec { B }$ is 4.00 units in length and points along the negative y-axis. Use graphical methods to find the magnitude and direction of the vectors $\overrightarrow { \mathbf { A } } + \overrightarrow { \mathbf { B } }$