Modelling Motion of Objects using various Equations

Modelling motion involves using physical principles and mathematical formulas and equations to describe the behaviour of an object as it moves.
The three fundamental concepts that are crucial for understanding motion are displacement, velocity, and acceleration.
Displacement is the change in position of an object and is represented by the variable ‘s’. It’s a vector quantity, meaning it has both magnitude and direction.
Velocity, represented by the symbol ‘v’, refers to the rate of change of displacement or how fast an object’s position is changing. Like displacement, velocity is also a vector quantity.
Acceleration, represented by the symbol ‘a’, denotes the rate of change of velocity or how fast an object’s speed is changing. It is another vector quantity.
An object moving in a straight line can be modelled using equations of linear motion. The three main equations of linear motion are:
1. v = u + at
2. s = ut + 1/2at^2
3. v^2 = u^2 + 2as Here, ‘u’ is the initial velocity, ‘v’ is the final velocity, ‘a’ is the acceleration, ‘s’ is the displacement, and ‘t’ is the time.
If an object is moving under the influence of gravity, it will experience a constant acceleration due to gravity represented as ‘g’. In this case, the equations of motion may be adjusted to include ‘g’ where ‘a’ used to be.
When dealing with an object’s motion in a circular path or circular motion, it becomes essential to consider the ‘centripetal’ or ‘radial’ acceleration. This is the acceleration of an object moving in a circular path and is always directed towards the centre of the path.
Centripetal acceleration can be expressed using the equation a = v^2 / r, where ‘v’ is the speed of the object, and ‘r’ is the radius of the circular path.
For objects moving in a plane rather than a straight line or a circle, vector addition and subtraction come into play. These are techniques that allow you to calculate the net effect of multiple motions in different directions.
Circular motion also involves the concept of ‘angular velocity’, denoted by omega (ω), which measures how quickly something is rotating or spinning.
In many cases, particularly where forces and energy are involved, integration and differentiation may also come into play in modelling motion.
It’s vital to remember that these equations model ideal situations and may not account for variables such as air resistance or friction in real-world situations.