Measurement, Conversions, & Mathematical Skills

Given the expression  $\frac{1}{2}mv^2=\frac{1}{2}kx^2$ , which of the following choices has correctly solved for the variable  $k$  ?

•  $k=\frac{mv^2}{x^2}$  

•  $k=\frac{mv}{x}$  

•  $k=\frac{1}{2}mv^2-\frac{1}{2}x^2$  

•  $\sqrt{\frac{2x^2}{mv^2}}$  

Given the equation $F=\frac{mv^2}{r}$ , if $m$  has units of [ $kg$ ],  $v$  has units of [ $\frac{m}{s}$ ], and $r$  has units of [ $m$ ], then which of the following would be the unit for  $F$  ?

•  $\frac{kg}{s^2}$  

•  $\frac{kg\cdot m^2}{s^2}$  

•  $\frac{kg\cdot m}{s^2}$  

•  $\frac{kg}{m^2}$  

Which of the following quantities represents the smallest value for time?

• 10 μs (microseconds)

• 1 ns (nanosecond)

• 500 ps (picoseconds)

• 0.01 ms (millisecond)

Which of the following quantities when expressed with a metric prefix is equivalent to $1.49\times10^{11}$  bytes? 

• 1.49 kilobytes

• 1.49 Terabytes

• 149 Gigabytes

• 149 Terabytes

Which of the following is NOT a fundamental unit?

• kilogram

• pound

• meter

• second

The electron has a rest mass of $9.11\times10^{-31}$ kg. Which order of magnitude best represents the electron's rest mass?

•  $10^{-30}\ kg$  

•  $10^{-31}\ kg$  

•  $10^{-32}\ kg$  

• None of these

The wavelength of green light is approximately 490 nm (nanometers). What is the order of magnitude of green light’s wavelength in meters?

•  $10^{-6}\ m$  

•  $10^{-7}\ m$  

•  $10^{-8}\ m$  

•  $10^{-9}\ m$  

If a room is 12 feet and 10 inches in length, which of the following choices is equivalent to this length? (Conversion Factor: 1 foot = 12 inches)

• 10 feet or 12 inches

• 12 feet or 10 inches

• 12.10 feet or 120 inches

• 12.8 feet or 154 inches

Which of the following units of measurement is NOT associated with the metric system?

• kilogram

• slug

• second

• centimeter

For the following equation, $\rho Vg\ -\ mg\ =\ ma$  which of the following correctly isolates $V$ ?

•  $V=\frac{ma}{\rho g}+\frac{m}{\rho}$  

•  $V=\frac{a+g}{\rho g}$  

•  $V=\frac{ma-mg}{\rho g}$  

•  $V=\frac{ma}{mg}-\rho g$