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Unit Analysis

Example 1: $V=V_0+at$
Example 2: $x=\frac{V}{3a}$

Note:
x=Distance (meters)
V = Distance/time ( meters/second )
a = Distance/ $time^2$ (m/ $s^2$ )
t=time (s)

A.) Is example 1 Dimensionally correct?

V= $v_0r \cdot a \cdot t$ Break equation into components/piecs

(m/s)=(m/s)+(m/ $s^2$ ) $\cdot$ s Cancel terms

m/s = m/s + m/s

m/s = m/s

B.) Is example 2 Dimensionally correct?

m= $\frac {m/s}{3 \cdot {m/s^2}}$ Remove the numbers

m= $\frac {m/s}{m/s^2}$

m= $\frac{s^2}{m} \cdot \frac{m}{s}$ Cancel terms

m=s Not True

Therefore, this equation is dimensionally incorrect!