# Physics 11 formula and representation sheet

Use only when the model assumptions fit the problem. Keep vector directions, SI units, and significant figures explicit.

## Vectors and graphs
- R_x=sum A_x, R_y=sum A_y, R=sqrtR_x^2+R_y^2
- slope =Delta y/Delta x; area meaning depends on axes/model

## Kinematics (constant acceleration)
- bar v=Delta x/Delta t
- a=Delta v/Delta t
- v_f=v_i+aDelta t
- Delta x=v_iDelta t+frac12aDelta t^2
- v_f^2=v_i^2+2aDelta x
- projectile components: v_0x=v_0costheta, v_0y=v_0sintheta
- near Earth: gapprox9.81,mathrmm/s^2 downward

## Dynamics
- sumvec F=mvec a
- F_g=mg
- F_k=mu_kN; F_slemu_sN
- F_s=-kx
- incline components: mgsintheta, mgcostheta

## Work and energy
- W=Fdcostheta
- E_k=frac12mv^2
- Delta E_g=mgDelta h
- W_mathrmnet=Delta E_k
- P=W/Delta t=Delta E/Delta t
- eta=E_mathrmuseful/E_mathrminputtimes100%
- MA=F_mathrmout/F_mathrmin

## DC circuits
- I=Delta Q/Delta t
- V=Delta E/Delta Q
- V=IR
- series: R_mathrmeq=sum R_i
- parallel: 1/R_mathrmeq=sum1/R_i
- KCL: sum I_mathrmin=sum I_mathrmout
- KVL: sumDelta V=0
- source model: V_mathrmterminal=mathcalE-Ir (discharging)
- P=IV=I^2R=V^2/R

## Thermal
- Q=mcDelta T
- isolated calorimetry model: sum Q=0

## Waves and sound
- v=flambda
- f=1/T
- beats: f_mathrmbeat=|f_1-f_2|
- fixed-fixed string: L=nlambda/2

## Evidence checks
- state system/coordinates; identify model conditions; carry units; report uncertainty; compare prediction with evidence; name model/method limitations.
