Kinematics: Motion in One Dimension

Basics of Kinematics and Motion

Kinematics is the branch of physics that describes the motion of objects without considering the cause of the motion.
Motion involves four key quantities: displacement, velocity, acceleration, and time.
Displacement is the change in position of an object and can be positive or negative.
Velocity is the speed of an object in a particular direction. Like displacement, it can also be positive or negative.
Acceleration is the rate at which an object changes its velocity.
And time, which measures the duration of the movement.

Understanding Displacement and Velocity

Displacement and velocity can be graphed together. The area under a velocity-time graph gives the displacement of the object.
Velocity is calculated as displacement divided by time, or v = d/t.
Speed is the absolute value of velocity.

Confounding Acceleration

Acceleration is calculated as change in velocity divided by time, or a = Δv/ t.
The slope of a velocity-time graph provides the acceleration of the object.

The Equations of Motion

There are three key kinematics equations used to relate displacement, velocity, acceleration, and time in one dimensional motion.
- v = u + at (final velocity equals initial velocity plus acceleration times time)
- s = ut + 1/2at² (displacement equals initial velocity times time plus half of the acceleration times time squared)
- v² = u² + 2as (final velocity squared equals initial velocity squared plus twice the acceleration times the displacement)
Graphs and equations are essential tools in understanding kinematic relationships.

Free-fall and Gravity

In free-fall problems, acceleration is due to gravity, which is approximately -9.8 m/s² on Earth.
The displacement of an object in free-fall under the influence of gravity alone can be calculated using the equations of motion, with the acceleration set equal to -9.8 m/s².
Free-fall problems often involve finding maximum height, total flight time, or final velocity upon landing.

Kinematics Vectors

Lastly, kinematics is also the basis for understanding vectors and vector addition, which is crucial for analysing motion in more than one direction.

It is critical to practice solving problems using these kinematic equations and principles. This will help develop a firm understanding of how objects move and how their motion can be predicted and analysed.