### 1-D

With the absence of air resistance*,* the idealized motion is called **free-fall** and the acceleration of a freely falling body is called the **acceleration due to gravity near surface of the earth**. All of the free fall objects withstand the same downward acceleration towards earth’s center.

Relative Motion: **Frame of Reference** is a coordinate system plus a timer

Velocity of Passenger Relative to Ground $=$ Velocity of Passenger relative to train $+$ Velocity of the relative to ground.

$V_{PG}= V_{PT}+ V_{TG}$

### 2-D

The two dimensional motion uses the vector addition / subtraction.

$\bigtriangleup V = V_{f}-V_{i}]-$ The velocity change (speed / direction) $A_{avg}= \bigtriangleup V /\bigtriangleup t$

While the instantaneous acceleration is defined as the limit as $\bigtriangleup t$ approaches 0 of $\bigtriangleup V /\bigtriangleup t$

$A_{a/b}= V_{a/t}+V_{t/b}$ where: a $=$ person, t $=$ transportation , b $=$ motion of another person

### Uniform Circular Motion

$V = 2\pi r/T$ where T represents the time elapsed, r $=$ radius from the center, and v $=$ the velocity accelerating towards the centre of the circle.

The speed in a uniform circular motion is always constant.

$\bigtriangleup V/V = v \bigtriangleup t/r$ $\bigtriangleup V/\bigtriangleup t=v_{2}/r$

Therefore:

$a_{centripital}= v_{2}/r$

$\ast$ As the acceleration aims towards the center, the $V_{tangent}$ always changes throughout the motion

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