Example 1.1 Analysis of an Equation Dimensions and Units of Four Derived Quantit

Question

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 +

Explanation / Answer

a = t^-1 b is dimensionless c is t^1

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