Question

which expression is dimensionally consistent with anexpression that would yield a value for time-1?(v is velocity, x is distance, and t istime)
a. v/x
b. v2/x
c. x/t
d. v2/t
e. x/v

Answer 1

Option A is the correct answer.

Explanation:

Here we need to find an expression that would yield a value for time⁻¹

We know that

              Velocity = Displacement ÷ Time

              v = x/t

Option A :

                 $\frac{v}{x}=\frac{\frac{x}{t}}{x}=\frac{1}{t}=t^{-1}$

               Option A is correct

Option B :

                 $\frac{v^2}{x}=\frac{\frac{x^2}{t^2}}{x}=\frac{x}{t^2}$

               Option B is not correct

Option C :

                 $\frac{x}{t}$

               Option C is not correct

Option D :

                 $\frac{v^2}{t}=\frac{\frac{x^2}{t^2}}{t}=\frac{x^2}{t^3}$

               Option D is not correct

Option E :

                $\frac{x}{v}=\frac{x}{\frac{x}{t}}=t$

               Option E is not correct

Option A is the correct answer.