Questions: Question 11 (2 points) Using dimensional analysis, which one of the following equations is dimensionally correct? In these equations, x has units of meters, t has units of seconds, v has units of meters per second, and a has units of meters per second squared. t^2=x / a x=a t v=2 a x x=v / t

Question 11 (2 points) Using dimensional analysis, which one of the following equations is dimensionally correct? In these equations, x has units of meters, t has units of seconds, v has units of meters per second, and a has units of meters per second squared. t^2=x / a x=a t v=2 a x x=v / t

Transcript text: Question 11 (2 points) Using dimensional analysis, which one of the following equations is dimensionally correct? In these equations, $x$ has units of meters, $t$ has units of seconds, $v$ has units of meters per second, and $a$ has units of meters per second ${ }^{2}$. $t^{2}=x / a$ $x=a t$ $v=2 a x$ $x=v / t$

Solution

Solution Steps

Step 1: Understand the Units of Each Variable

$ x $ has units of meters $[m]$.
$ t $ has units of seconds $[s]$.
$ v $ has units of meters per second $[m/s]$.
$ a $ has units of meters per second squared $[m/s^2]$.

Step 2: Analyze Each Equation for Dimensional Consistency

Equation 1: $ t^2 = \frac{x}{a} $

Left side: $ t^2 $ has units $[s^2]$.
Right side: $\frac{x}{a} = \frac{[m]}{[m/s^2]} = [s^2]$.
Both sides have the same units $[s^2]$, so this equation is dimensionally correct.

Equation 2: $ x = a t $