### Physics derivations

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All derivations required for Physics leaving certificate, only an indicator is given that should be all one needs, the rest is algebra.

1

v = u + at

a = v-u/t, rearrange this.

2

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

3

V^2 = U^2 + 2as

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

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

4

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

5

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

6

Relationship between periodic time and radius for a satellite in orbit

7

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

8

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

9

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

10

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

11

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

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