Motion in One Dimension

I think it was about a week ago or so that I declared chapter two of University Physics, by Young and Freeman, dead.  I had been sauntering through it for months.  The main points are easy, although as usual the application of them into concrete situations is more diffiicult.  But here I summarize the main points:

1. Average velocity Δx/Δt or (x2-x1)/(t2-t1).

2. Instantaneous velocity is lim Δt→0 of Δx/Δt, which = dx/dt.

3. Average acceleration Δv/Δt or (v2-v1)/(t2-t1).

4. Instantaneous acceleration is lim Δt→0 of Δv/Δt, which = dv/dt.

Then these equations work for constant acceleration
5. v₂ = v₁ + at

6. x₂ = x₁ + vt + ½at²

7. v₂² = v₁² + 2a(x₂-x₁)

8. x₂ - x₁ = [(v₂ + v₁)/2]t

9. Finally, for varying acceleration, one will have to integrate:

x₂ = x₁ + ∫0→t of v dt

v₂ = v₁ +∫0→t of a dt