##### Physics derivations

v = u + at

a = v-u/t, rearrange this.

s = ut + 1/2at^2

Average velocity = initial + final velocity/2 ... u + v / 2

v = u+ at

u + u + at/2

(u + u + at/2) (t) = s

V^2 = U^2 + 2as

We know v = u + at... Square both sides then factorise out 2a,

then sub s = u+1/2at^2

F = ma is a special case of Newtons second law

Force is proportional to the rate of change of momentum

F <( (Change of momentum/time, turn that into acceleration

F <( ma

F = k(ma) ...k = 1

F = ma

v = rω

We define Theta (radians) as (length of the arc) / radius : 0 =
s/r

Divide both sides by t, 0/t = s/tr

But ω = 0/t and v =
s/t… ω = v/r

Cross multiply, v = rω

Relationship between periodic time and radius for a satellite in orbit

To show that any object that obeys hookes law will also execute simple harmonic motion

Hooke’s law: F <( -s F = -k s

But F = ma, therefore ma = -k
s

divide both sides by m : a = (-k/m)s …. This is an equivalent
to the equation for S.H.M

Diffraction grating formula: n = d Sin

Draw a diagram of the diffraction grating

From it we can see
that for constructive interference to occur, the extra path length
that the top ray travels must be an integer number of wavelengths, i.e
(n)

Using trigonometry, this extra path length is equal to dsin0,
where d is the slit width

Derive an expression for the effective resistance of the two resistors connected in series.

Effective resistance = R1 + R2

Apply Ohm’s law to each
resistor:

V1 = I(R1)

V2 = I(R2)

Since the voltages are
in series :

Voltage total = V1 + V2

Derive an expression for the effective resistance of the two resistors connected in parallel

1/Rtotal = 1/R1 + 1/R2

Apply Ohms law to each
resistor

V/Rtotal = V/R1 + V/R2, divide across by V for the equation

Force on a moving charge, F = Bqv

Draw a diagram of a conductor of length L

If q is the charge
which carries the current in this section of the conductor, then I =
q/t., the average velocity with which the charge flows is given by v =
l/t

Substituting into the primary equation we have for force, we
get

F = B x q/t x vt