Intro to Kinematics for Middle-to-High Schoolers -- from a High Schooler
Part 1
The first thing I thought of when we first started learning kinematics was kinetic sand. Now, I know why it’s called kinetic sand.
Alola! Welcome to the fascinating world of kinematics, the branch of physics focused on motion without considering the forces behind it. This brief overview serves as an introductory guide for middle to high school students, requiring no prior knowledge of physics. Understanding kinematics is crucial, not just as a foundation for more advanced physics topics, but also for real-world applications in fields such as engineering, robotics, sports science, and yellow-light physics. By mastering these concepts, we will develop analytical skills to predict and analyze motion in various contexts. This leads to projectile and circular motion, as well as being complemented by dynamics and universal gravitation.
Let’s learn about Uniform Motion, Non-Uniform Motion, Strategies for Problem Solving, and designing v-t (velocity-time) and a-t (acceleration-time) graphs.
Motion falls within three categories: Uniform, Non-Uniform (UA), and Complex.
UA stands for “Uniformly Accelerated”, meaning the a-t graph in non-uniform motion will be constant.
Equations of motion can easily be derived from graphs of motion, and there is a very simple process to do that. We will derive this later.
For now, remember any linear graph has the form:
y = mx+c,
where
y represents the y value at any x,
x represents any value along the x axis (which will be time for us),
m represents the slope of the graph, also defined as for every X of x, y changes by Y,
c represents the y-intercept, also defined as when x is 0, y is Y
Let’s define each type of motion in terms of words, graphs, and equations.
Lesson One - Definition of Uniform Motion
Uniform motion is a type of motion where the object is moving at a constant speed; neither slowing down nor speeding up.
In this motion, since the object is moving at a constant speed, its position is changing at a constant rate, and its velocity has the same magnitude throughout the time the motion is occuring. So, the distance(position)-time graph (or d-t graph) will be a straight line, while the velocity time graph (or v-t graph) will be a horizontal line.
To define uniform motion using equations, recall that if a is proportional to b, that means that the graph’s slope must be constant throughout, which we defined when we explained it graphically. So, because d-t is linear, that means d is proportional to t, so d/t is a constant (definition of direct proportionality). Similarly, the definition of velocity is the distance traveled per unit of time (remember ‘for every X of x, y changes by Y’ previously?), so we derive
v=d/Δt
speed = distance/change in time (note distance is a scalar, so we take scalar version of speed),
And if we were concerned with deltas, then
v=Δd/Δt
Lesson Two - Definition of Non-Uniform Motion (Uniformly Accelerated)
Non-Uniform motion (UA) is a type of motion where the object is uniformly accelerated; either slowing down or speeding up.
In this motion, since the object is either slowing down or speeding up, its position is changing in a quadratic form, and its velocity has a different magnitude throughout the time the motion is occurring. So, the d-t graph will be a curved line, while the v-t graph will be a straight line.
If a is proportional to b, that means that the graph’s slope must be constant throughout, which we defined when we explained it graphically. So, because v-t is linear, v is proportional to t, so v/t is a constant (definition of direct proportionality). Similarly, the definition of acceleration is the change in velocity per unit of time, so we can construct:
a=Δv/Δt
acceleration = velocity/change in time (note this equation is always a vector because you either accelerate to the left of the right)
In the next two (short) lessons, let’s have a brief on Complex Motion and Strategies for Problem-Solving in Kinematics!!