For each question, show sufficient work to justify your answer. Answers without work will not receive credit.

Compute the total number of minutes in $3$ weeks.

What is the total mass of $1\mathrm{.}02kg+8\mathrm{.}65g$ in grams? Ignore significant figures for this question.

For the following equation, $m$ is mass, $a$ is acceleration, $v$ is velocity, and $x$ is displacement. All are measured in meters$-$kilograms$-$seconds $($MKS$)$ units. Note: units and dimensions are different.

$ma=-bv-kx$

a$)$ What are the units of $b?$

b$)$ What are the dimensions of $k?$

Consider the following equation, where $t($with units of $s)$ is the independent variable, $(s-s0)($with units of meters$)$ is the dependent variable, and $v$ and a are constants:

$(s-s0)=vt+\frac{1}{2}a{t}^2$

a$)$ Write the linearized equation. $(y=Ax+B$ form$)$ Note: pay attention to what variable is dependent vs$.$ independent.

b$)$ What is the slope of the linearized equation?

c$)$ What is the $y-$intercept?

Consider the following equation, where $m($with units of grams$)$ is the independent variable, $T($with units of $s)$ is the dependent variable, and $2,k,$ and $p$ are constants:

$T=2\sqrt[\phantom{2}]{\frac{m}{k}+\frac{p}{k}}$

a$)$ Write the linearized equation. form