VCE Physics/Unit 2/AoS 1/Kinematics

Introduction
Kinematics is really just a fancy word for "motion". You could accuse physicists of making up fancy words just to sound smart or deliberately confuse you when you're trying to learn physics. However, using the word kinematics comes with the extra implication that we are not just going to talk about motion as you might in everyday life ("Hey, I walked to the shops today!") but we are going to understand the mathematics that can be used to escribe motion. Also, we specifically use "kinematics" to describe the study of how things move without worrying about why they are moving or changing their motion (see the "dynamics" section for that). This might seem impossible, but it turns out that all motion is the same, in the sense that we can use the same mathematics to describe any motion whether it is a ball thrown by us, a car driven by an engine, or gravity causing an apple to fall. However, the mathematics can get quite complicated. So in this course we're only going to deal with kinematics in 1-dimension (1D). That means we only need one number to describe the position of an object. This might involve, for example, a train movnig up and down a straight train track, a car driving up and down a straight road. Can you think of other examples of 1D motion?

Position, distance and displacement
So, if we have a 1D scenario it is relatively simple to use mathematics to describe where the object is. Imagine a car driving up and down a straight road. We are going to define an axis (a line with numbers). We'll use the letter x to represent this axis. We first define an origin (a place we are going to call zero). Then we decide which way is going to be positive numbers and which way negative. And we define a scale... we'll use m. See diagram below.

At any point in time we can give a value for x, where the car is on the x-axis.

etc.

Time
Rather than simply discussing a single point, or just several points, for a particular time, it can be interesting to look at how the position of the car is varying over time. Now if we track all the points on the one line the points will cover each other up and we cannot see them. So if we make a copy of the line for different times we can then see how the car moves over time. We can make a large number of copies of the line... but lets remove the lines, just keep one copy of the line for reference... and we have a "graph" of the position of the car over time. We are now tracking the position of the car in 2D - 1-dimension of space and 1-dimension of time.

You need to get used to looking at a graph of an objects motion like this, and being able to describe what the object is doing. So, let's take some simple cases.

Case 1 - object not moving Case 2 - object continually moving in the same direction.

Can we have a vertical line? What does the steepness of the line represent?

Velocity and speed
Velocity = gradient of slope on graph. Constant velocity straight line. Changing velocity, gradient of line changes. v = delta x / delta t

Acceleration
Acceleration = change in velocity. Deceleration = colloquialism for acceleration opposite direction of motion (NOT negative acceleration).

Non-uniform motion
Well, if uniform motion is constant acceleration, it should be fairly obvious that non-uniform motion is non-constant acceleration. The equations you have

Relevant dot points from the Study Design

 * identify parameters of motion as vectors or scalars
 * analyse graphically, numerically and algebraically, straight-line motion under constant acceleration:
 * $$v = u + at$$, $$v^2 = u^2 + 2as$$, $$s = frac{1}{2}\left(u + v\right)t$$, $$s = ut + frac{1}{2}at^2$$, $$s = vt - frac{1}{2}at^2$$


 * graphically analyse non-uniform motion in a straight line