Question

Is t=v/x dimensionally consistent? why?

Answer 1

Although not specified but I assume that

t = time , v = velocity and x = position

For an equation to be dimensionally correct the dimension on the right hand side and left hand side of eqauation must be equal.

Unit of t is second , thus dimension of t will be [T]

Unit of v is meter/second , thus dimension of v will be [LT^{​​​​​-1}​​​]

Unit of x is meter , thus dimension of of x will be [L]

According to eqauation

t = v/x

[T] = [LT^{​​​​​-1}] / [L]

[T] = [T^{​​​​​​-1}​]

HERE LHS IS NOT EQUAL TO RHS , THUS EQUATION IS NOT DIMENSIONALLY CONSISTENT.