Chapter 2: Kinematics

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