Speed and Velocity

Distance: Distance is the length between two points or objects.

It is a scalar quantity, meaning it only has magnitude and no direction.

Symbol: $X$ or $S$

SI Unit: Meter (m)

Displacement: Displacement refers to the distance between two points in a specific direction.

It is a vector quantity, meaning it has both magnitude and direction.

Speed	Velocity
Is the rate of change of distance	Is the rate of change of displacement
It is a scalar quantity	It is a vector quantity
It only has magnitude	It has both magnitude and direction
It is always positive or zero	It can be positive, negative, or zero
Speed is measured in meters per second (m/s)	Velocity is measured in meters per second (m/s)
It does not consider direction	It considers direction

The SI unit of speed and velocity is m/s.

i. Initial velocity (U)

Initial velocity refers to the velocity of a body at the start of observation. It is the speed and direction of an object at the beginning of the time interval under consideration. The symbol used for initial velocity is U.

ii. Final velocity (V)

Final velocity refers to the velocity of a body at the end of the observation period. It represents the speed and direction of the object at the end of the time interval. The symbol used for final velocity is V.

iii. Average velocity

Average velocity is the mean or average of the initial and final velocities, or it can also be defined as the ratio of the total displacement to the total time taken. It is given by the formula:

$$\text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}}.$$

It provides a measure of the object's overall motion during a specific period.

iv. Uniform or constant velocity

Uniform or constant velocity refers to motion where the rate of change of displacement with time remains constant. In other words, the object moves equal distances in equal intervals of time. The object does not accelerate or decelerate but continues at a steady pace. The velocity remains constant throughout the motion.

v. Absolute velocity

Absolute velocity is the actual velocity of a moving object as recorded by a stationary observer. It is the true velocity of an object with respect to the earth or another reference point in space. This velocity is typically considered in a reference frame where the observer is at rest.

vi. Relative velocity

Relative velocity refers to the velocity of an object as observed from another moving object. It depends on the motion of the two objects with respect to each other. For two objects A and B, moving with velocities $V_A$ and $V_B$, the relative velocity of A with respect to B is given by:

$$\text{Relative Velocity} = V_{A} - V_{B}.$$

This is important for analyzing the motion of objects when viewed from different frames of reference.

vii. Instantaneous velocity

Instantaneous velocity is the velocity of a moving object at a specific point in time. It is the rate of change of displacement with respect to time at any given moment. Mathematically, instantaneous velocity is the limit of average velocity as the time interval approaches zero. It is given by the derivative of displacement with respect to time:

$$\text{Instantaneous Velocity} = \frac{d\text{Displacement}}{dt}.$$

This type of velocity is crucial in calculus-based physics, where the velocity of an object is analyzed at every moment in time.