1. | Given mv = Ft, where m is mass, v is speed, F is force, and t is time, what are the dimensions of each side of the equation? Is the equation dimensionally correct? | [left side] = M·L/T
[right side] = M·L/T Therefore the equation is dimensionally correct. |

2. | Given H = mCDT, where H is in joules, m in kilograms, and DT in kelvin, what are the SI units and dimensions of C? | Since C = H/(mDT), the SI units
are J·kg^{-1}·K^{-1}.
[C] = (M·L ^{2}·T^{-2})·M^{-1}·q^{-1}
= L^{2}·T^{-2}·q^{-1} |

3. | Given P = kADT/l, where A is the area, DT is difference in temperature, l is length, and k is a constant with SI units of watts pr (metre·kelvin), what are the SI units for P (rate of thermal energy flow)? | Recall that watt (W) is joules per second, so [k] = M·L·T^{-3}·q^{-1}.
[A] = L ^{2}, [DT] = q
, and [l] = L
[right side] = M·L ^{2}/T^{3}
Therefore, [P] = M·L ^{2}/T^{3}, and SI units
are kg·m^{2}/s^{3}, or J/s. |

4. | Given E = a sin (bt), where E is energy, is length and t is time: (a) What are the dimensions and SI units of b? | [b] = T^{-1}
Remember that the argument of the sine function must be dimensionless. Since the argument in this case is an unknown (b) multiplied by time (t), then b must have dimensions of inverse time. The SI units of "b" are s ^{-1}. |

(b) What are the dimensions and SI units of a? | [a] = [E/] = M·L/T^{2},
since sine is dimensionless. The SI units of "are" are kg·m/s^{2},
or newton. |