(1) The equation is
[tex]v_2=v_1+a\Delta t[/tex]
For v_1,
[tex]\begin{gathered} v_2=v_1+a\Delta t \\ Subtract\text{ a}\Delta t\text{ on both sides.} \\ v_2-a\Delta t=v_1+a\Delta t-a\Delta t \\ v_2-a\Delta t=v_1 \end{gathered}[/tex]
For a,
[tex]\begin{gathered} v_2=v_1+a\Delta t \\ \text{Subtract v}_1\text{ on both sides} \\ v_2-v_1=v_1-v_1+a\Delta t \\ v_2-v_1=a\Delta t \\ \text{Divide }\Delta t\text{ on both sides.} \\ \frac{v_2-v_1}{\Delta t}=a\frac{\Delta t}{\Delta t} \\ \frac{v_2-v_1}{\Delta t}=a \end{gathered}[/tex]
For time,
[tex]\begin{gathered} v_2=v_1+a\Delta t \\ \text{Subtract v}_1\text{ on both sides} \\ v_2-v_1=v_1-v_1+a\Delta t \\ v_2-v_1=a\Delta t \\ \text{Divide }a\text{ on both sides.} \\ \frac{v_2-v_1}{a}=\frac{a}{a}\Delta t \\ \frac{v_2-v_1}{a}=\Delta t \end{gathered}[/tex]
