To be dimensionally consistent,distance [L],acceleration [L/T²],and time [T] must be related as follows. A) distance = acceleration² $\times$ time² B) distance = acceleration $\times$ time C) distance = acceleration $\times$ time² D) distance = acceleration² $\times$ time

Question

Quizplus · Accepted Answer

To be dimensionally consistent, we need to ensure that the units on the left and right sides of the equation match. 
Distance is in units of L (length), acceleration is in units of L/T^2 (length per time squared), and time is in units of T (time). 
Therefore, the equation needs to have distance on one side, and acceleration multiplied by time (or some power of time) on the other side to cancel out the units of time in acceleration. 
Option C has the correct units and is the only one that satisfies this condition.

To Be Dimensionally Consistent,distance [L],acceleration [L/T2],and Time [T] Must Be ×\times×

To Be Dimensionally Consistent,distance [L],acceleration [L/T²],and Time [T] Must Be $\times$