By failing to prepare, you are preparing to fail.

# Physics

/Tag: Physics
21 03, 2018

## Challenging Rates

Challenging Rates Questions The first snow of the season begins to fall during the night. The depth of the snow, h, increases at a constant rate through the night and the following day. At 6 am a snow plough begins to clear the road of snow. The speed, [...]

27 01, 2017

## Motion in One Dimension

Motion in One Dimension Proof of $a=v.\frac{dv}{dx}$ we know $a=\frac{dv}{dt}$ and $v=\frac{dx}{dt}$ $a=v.\frac{dv}{dt}.\frac{1}{v}$ since $v=\frac{dx}{dt}$, then $\frac{1}{v}=\frac{dt}{dx}$ $a=v.\frac{dv}{dt}.\frac{1}{v}$ ⇒ $a=v.\frac{dv}{dt}.\frac{dt}{dx}$ ∴ $a=v.\frac{dv}{dx}$ worked examples further examples = 10x + 15 - 7x + 14 = 3x + 29 harder examples u = 1 [...]

17 10, 2016

## Differential Proof

Differential Proof A = A0ekt $\frac{dA}{dt}=kA$ worked examples  Show that A = A0ekt, where A0 is the initial population is a solution to the equation $\frac{dA}{dt}=kA$.  $\frac{dA}{dt}=k\times A_oe^{kt}$ since integrating this is beyond the scope of the course, we differentiate and show that the differential is right, so it must mean [...]

20 08, 2015