Answer :
Answer:
- [tex]v_o=v_f-at[/tex]
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Given equation
- [tex]a=\cfrac{v_f-v_0}{t}[/tex]
Solve it for [tex]v_0[/tex]
Step 1
Multiply both sides by t to get rid of fraction:
- [tex]at=v_f-v_o[/tex]
Step 2
Find [tex]v_0[/tex] by rearranging the terms:
- [tex]v_o=v_f-at[/tex]
Correct choice is the last one.
Answer:
[tex]v_0=v_f-at[/tex]
Step-by-step explanation:
Given equation:
[tex]a=\dfrac{v_f-v_0}{t}[/tex]
To solve for v₀, rearrange the equation to isolate v₀.
[tex]\textsf{Multiply both sides by $t$}:[/tex]
[tex]\implies at=\dfrac{\left(v_f-v_0\right)t}{t}[/tex]
[tex]\textsf{Cancel the common factor $t$ on the right side}:[/tex]
[tex]\implies at=\dfrac{\left(v_f-v_0\right)\diagup\!\!\!\!t}{\diagup\!\!\!\!t}[/tex]
[tex]\implies at=v_f-v_0[/tex]
[tex]\textsf{Add $v_0$ to both sides}:[/tex]
[tex]\implies at+v_0=v_f-v_0+v_0[/tex]
[tex]\implies at+v_0=v_f[/tex]
[tex]\textsf{Subtract $at$ from both sides}:[/tex]
[tex]\implies at+v_0-at=v_f-at[/tex]
[tex]\implies v_0=v_f-at[/tex]
Solution
[tex]\large\boxed{v_0=v_f-at}[/tex]