Deriving kinematic equations
1) xf=xi+bit+1/2at^2 don't need to use vf
2) xf=xi+1/2(xi+vf)t don't need to use a
3) vf=vi+at don't need to use xf
4) vf^2=vi^2+2a(xf-xi)
use the three kinematic equations (re-work to make them look like these). i got #s 2 and 3, but i'm stuck on 1 and 4.

Some material consisting of a collection of microscopic objects is kept at a high temperature. a photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of 0.3 ev, 0.5 ev, 0.8 ev, 2.0ev, 2.5ev, and 2.8ev. these are the only photon energies observed. (a) draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. on the diagram, indicate the transitions corresponding to the emitted photons. explain briefly. (b) would a spring–mass model be a good model for these microscopic objects? why or why not? (c) the material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. what photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? explain briefly.

The freezing and boiling point of a substance changes as the air pressure around it changes. for example, at a lower air pressure (higher altitude) it is easier for water molecules to escape from liquid into the air. in a high altitude city such as denver, colorado compared to a sea-level city such as houston, texas, water

What is friction? how does it affect the motion of an object?