Question

The question is in the image. Ignore the color underneath each possible answer, that is what I am supposed to do(I am supposed to color in). The question is hard for me.

Answer 1

`v_0=v_f-at`

Explanation:

Given equation:

`a=(v_f-v_0)/(t)`

To solve for v₀, rearrange the equation to isolate v₀.

`\textsf{Multiply both sides by $t$}:`

`\implies at=(\left(v_f-v_0\right)t)/(t)`

`\textsf{Cancel the common factor $t$ on the right side}:`

`\implies at=(\left(v_f-v_0\right)\diagup\!\!\!\!t)/(\diagup\!\!\!\!t)`

`\implies at=v_f-v_0`

`\textsf{Add $v_0$ to both sides}:`

`\implies at+v_0=v_f-v_0+v_0`

`\implies at+v_0=v_f`

`\textsf{Subtract $at$ from both sides}:`

`\implies at+v_0-at=v_f-at`

`\implies v_0=v_f-at`

Solution

`\large\boxed{v_0=v_f-at}`

Answer 2

• 
  `v_o=v_f-at`

=================================

Given equation

• 
  `a=\cfrac{v_f-v_0}{t}`

Solve it for
`v_0`

Step 1

Multiply both sides by t to get rid of fraction:

• 
  `at=v_f-v_o`

Step 2

Find
`v_0` by rearranging the terms:

• 
  `v_o=v_f-at`

Correct choice is the last one.