If in the international system of units $[ x ] _ { \mathrm { SI } } = \mathrm { m } , [ t ] _ { \mathrm { SI } } = \mathrm { s } , [ v ] _ { \mathrm { SI } } = \mathrm { m } / \mathrm { s }$, and $[ a ] _ { \mathrm { SI } } = \mathrm { m } / \mathrm { s } ^ { 2 }$, and (i) $x$ $= v t + a$, (ii) $x = \frac { 1 } { 2 } a t ^ { 2 }$, and (iii) $t = \left( \frac { 2 x } { a } \right) ^ { \frac { 1 } { 2 } }$, the dimensionally consistent equation(s) is(are):
A) (i), (ii), and (iii).
B) (i) and (iii).
C) (i) and (ii).
D) (ii) and (iii).
E) only (i).

Question

Quizplus · Accepted Answer

Equation (ii) and (iii) are dimensionally consistent. In (ii), both sides have dimensions of length. In (iii), both sides have dimensions of time. Equation (i) is not dimensionally consistent as the dimensions on both sides do not match.

If in the International System of Units [x]SI=m,[t]SI=s,[v]SI=m/s[ x ] _ { \mathrm { SI } } = \mathrm { m } , [ t ] _ { \mathrm { SI } } = \mathrm { s } , [ v ] _ { \mathrm { SI } } = \mathrm { m } / \mathrm { s }[x]SI​=m,[t]SI​=s,[v]SI​=m/s

If in the International System of Units $[ x ] _ { \mathrm { SI } } = \mathrm { m } , [ t ] _ { \mathrm { SI } } = \mathrm { s } , [ v ] _ { \mathrm { SI } } = \mathrm { m } / \mathrm { s }$