# The left hand side is a length, of dimensions L. The answer you have given would give the corresponding term dimensions of L / T. c =

Example 1.1 Analysis of an Equation Dimensions and Units of Four Derived Quantities Quantity Area Volume Speed Acceleration Dimensions L2 L3 L/T L/T2 SI units m2 m3 m/s m/s2 U.S. customary units ft2 ft3 ft/s ft/s2 Show that the expression v = at, where v represents speed, a acceleration, and t an instant of time, is dimensionally correct. SOLVE IT Identify the dimensions of v from the table above: [v] = L T Identify the dimensions of a from the table above and multiply by the dimensions of t: [at] = L T2 T = L T Therefore, v = at is dimensionally correct because we have the same dimensions on both sides. (If the expression were given as v = at2, it would be dimensionally incorrect. Try it and see!) MASTER IT HINTS: GETTING STARTED | I’M STUCK! Suppose you are given the following equation, where xf and xi represent positions at two instants of time, vxi is a velocity, ax is an acceleration, t is an instant of time, and a, b, and c are integers. xf = xita + vxitb + axtc For what values of a, b, and c is this equation dimensionally correct? a =

Treat the units for each quantity as algebraic quantities and take into account their cancellation. The right and left sides of the equation must have the same units throughout. b = L

The left hand side is a length, of dimensions L. The answer you have given would give the corresponding term dimensions of L / T. c =

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