Kinematics of Motion in a Straight Line

Basic Definitions

Motion refers to the change in position of an object with respect to its surroundings in a given period of time.
Displacement is the shortest distance from the initial to the final position of a point. It is a vector quantity, with both magnitude and direction.
Speed is the rate of change of distance. It is a scalar quantity, meaning it has magnitude but no direction.
Velocity is the rate of change of displacement. It is a vector quantity, possessing both a magnitude (speed) and a direction.
Acceleration is the rate of change of velocity. It is a vector quantity and can be positive (increasing velocity), negative (decreasing velocity) or zero.

The first equation of motion (v=u+at) relates velocity, initial velocity, time and acceleration.
The second equation of motion (s=ut+1/2at^2) provides an association between initial velocity, acceleration, time and distance travelled.
The third equation of motion (v^2=u^2+2as) depicts the relationship of initial velocity, acceleration, distance travelled and final velocity.

A Distance-Time graph depicts displacement over time. The slope of a distance-time graph gives velocity.
A Velocity-Time graph portrays velocity over time. The slope of a velocity-time graph provides acceleration, and the area under velocity-time graph gives displacement.

Relative velocity is the velocity of one object as observed from another object. It’s calculated by adding or subtracting the velocities depending upon their direction of motion.

In the context of kinematics, there are special cases known as free falling bodies where acceleration is due to gravity (denoted as ‘g’).
Upward motion (against gravity) is considered as negative acceleration (-g), while downward motion (with gravity) is figured as positive acceleration (+g).