Problem 1
At time $t=0$, an electron is at position $\vec{r}=0$ and has a velocity  $\hat{y}$ m/s. The electron is in an electric field of  $\hat{x}$ V/m. Where is the electron at time $t=$  s?

$\vec{r} = $ $\hat{x} + $ $\hat{y} + $ $\hat{z}$ [m]

Electron mass = $9.10938356 \times 10^{-31}$ kg  Electron charge = $-1.6021766208 \times 10^{-19}$ C

Problem 2

The position vector of a partcle is,

Here $t$ is the time in seconds. The total force acting on the particle is , where $x$ is the position in meters and $v$ is the velocity in m/s. How much work must be performed to move the particle between time $t=0$ and $t=$  s?

Problem 4

The position of a supersonic airplane is given by:

Here $t$ is the time in seconds. Where along the $x$-axis ($y=z=0$) is the sonic boom heard at time $t=0$?

$x=$ [m]

The speed of sound is $c=$ 340 m/s.

Problem 5
A thin lens with a focal length of  cm is placed between a slide and a projection screen. The screen is  meters from the lens. How far from the lens should the slide be placed so that the image is in focus on the screen?

$d=$  cm

What is the magnification of the image?

$m=$

Problem 6

Two-dimensional waves are sent out from the point $\vec{r}_1=-2\hat{x}$ [m]. These waves are described by,

Plot the wave that is observed at $\vec{r}=2\hat{x}$ [m].

Plot the wave along the $y$-axis at time $t=0$.