Question

in emilys physics class, she had to solve the equation ( 9 = \frac{1}{2} at^2 + ut ) for ( u ). each step of her work is shown below

use the drop-down menus to explain each step

given equation ( 9 = \frac{1}{2} at^2 + ut )

step 1 ( 9 - \frac{1}{2} at^2 = ut )

drop-down drop-down on both sides of the equation

step 2 ( \frac{9 - \frac{1}{2} at^2}{t} = u )

drop-down drop-down on both sides of the equation

Explanation:

Step 1: Subtract $\frac{1}{2}at^2$

To isolate the term with \( u \), we subtract \(\frac{1}{2}at^2\) from both sides of the equation \( 9 = \frac{1}{2}at^2 + ut \). This gives \( 9 - \frac{1}{2}at^2 = ut \).

Step 2: Divide by \( t \)

To solve for \( u \), we divide both sides of the equation \( 9 - \frac{1}{2}at^2 = ut \) by \( t \) (assuming \( t
eq 0 \)). This gives \( \frac{9 - \frac{1}{2}at^2}{t} = u \).

Answer:

• Step 1: Subtract \(\boldsymbol{\frac{1}{2}at^2}\)
• Step 2: Divide by \(\boldsymbol{t}\)