Question

when to use:

Answer 1

\[v= v _{0} = at\]
\[v _{ave}=((v+v _{0}) \div (2))\]
\[d= v _{0}t + ((at ^{2}) \div (2))\]
\[v ^{2}= v _{0}^2 + 2ad\]

Answer 2

Use these equations when you know the values of all other variables except one.
For example, you can use the first one if you want to know the final velocity having already known the initial velocity, the acceleration and the time for which the object has been accelerating.
Similarly, the second one is used when you want to know the average velocity of an object moving under constant acceleration when you know the final and the initial velocities.
You can use the other two equations in the same way.
In summary, you use an equation if it has only one unknown.

Answer 3

Use only for uniform acceleration motion. That is motion with a constant net force.

Do not use in other cases, such as:
- circular motion (even steady)
- harmonic motion (force is not uniform)
- motion in non uniform g- or E-field
- planets and satellites
- motion in magnetic fields

Actually, uniform acceleration is pretty limitative, but is over exceedingly used in school-type problems.
Only a small fraction of a motion can usually, if so, be considered as uniformly accelerated.