Kinematics

Basic Concepts

Kinematics is a branch of mechanics that investigates the motion of objects without considering the forces that cause the motion.
Distance is a measure of total path covered by an object irrespective of the direction, while displacement refers to the overall change in position of an object.
Speed is defined as the rate of change of distance with respect to time, whereas velocity is the rate of change of displacement with time. Velocity takes into account direction.
Acceleration is the rate of change of velocity with respect to time. If it is positive, velocity is increasing. If negative, velocity is decreasing.

There are three main equations of motion, also known as kinematic equations.
The first equation of motion: v = u + at, where v is the final velocity, u is the initial velocity, a is acceleration, and t is time.
The second equation of motion: s = ut + 0.5at^2, where s is displacement.
The third equation of motion: v^2 = u^2 + 2as.

Projectile motion >ccurs when an object with initial velocity is subject to an acceleration due to gravity.
The path followed by a projectile is known as trajectory.
The peak height reached by a projectile is called maximum height and the horizontal distance covered is range.
The time of flight (total time the projectile stayed in air) and maximum height are independent of the range.

Graphs of motion help us visualise changes in velocity, acceleration and displacement.
Gradient of a displacement-time graph gives velocity. Similarly, the gradient of a velocity-time graph gives acceleration.
The area under a velocity-time graph reveals displacement.
When dealing with rapidly changing acceleration (or jerk), jerk-time graphs can be used.