Velocity

What is Velocity?

Velocity describes how quickly an object's position changes with time and in what direction. Unlike speed, which only describes how fast an object moves, velocity also includes the object's direction of motion. Velocity is therefore important for describing the complete motion of an object.

What are the Symbol and SI Unit of Velocity?

The standard symbol for velocity is v. Its SI unit is meters per second (m/s). Other units, such as km/h, can also be used.

What is Velocity as a Vector Quantity?

Velocity is a vector quantity, meaning it has both magnitude and direction. For example, 20 m/s east describes a velocity, while 20 m/s by itself describes only a speed.

What is Average Velocity?

Average velocity is the total displacement divided by the total time taken:

average velocity = displacement / time

or:

v_avg = Δx / Δt

where Δx is the change in position and Δt is the time interval.

For example, if an object moves 100 m east in 5 s:

v_avg = 100 / 5 = 20 m/s east

What is Instantaneous Velocity?

Instantaneous velocity is an object's velocity at a particular moment in time. Unlike average velocity, which describes motion over a time interval, instantaneous velocity describes the motion at one specific instant.

In calculus, instantaneous velocity is the rate of change of position with respect to time:

v = dx/dt

What are Positive and Negative Velocity?

The sign of velocity depends on the chosen positive direction. If east is defined as positive, a velocity of +10 m/s means 10 m/s east, while -10 m/s means 10 m/s west.

A negative velocity does not mean the object is necessarily slowing down. It means the object is moving in the negative direction.

What is the difference between Velocity and Speed?

Speed and velocity are related but different.

Speed = how fast an object moves

Velocity = how fast an object's position changes and in which direction

Speed is a scalar quantity, while velocity is a vector quantity.

An object's average speed can be different from the magnitude of its average velocity.

What are Velocity and Displacement?

Velocity is directly related to displacement. Average velocity is calculated using displacement rather than total distance:

v_avg = Δx / Δt

For example, if a person walks 10 m east and then 4 m west in 7 s:

Total distance = 14 m

Displacement = 6 m east

Average speed = 14 / 7 = 2 m/s

Average velocity = 6 / 7 ≈ 0.86 m/s east

What are Velocity and Acceleration?Acceleration describes how quickly velocity changes with time:

a = Δv / Δt

Therefore, an object can accelerate by changing its speed, direction, or both.

For example, an object moving at a constant speed in a circular path is still accelerating because its direction of velocity continuously changes.

What is Velocity-Time Graph?

A velocity-time graph shows how velocity changes with time. The gradient (slope) of the graph represents acceleration.

The area under a velocity-time graph represents the object's displacement over that time interval.

What is Constant Velocity?

An object has constant velocity when its velocity remains unchanged in both magnitude and direction. This means the object moves in a straight line at constant speed.

If either its speed or direction changes, its velocity changes.

What are the Important Facts about Velocity?

Velocity describes the rate of change of position with time and includes direction. It is a vector quantity with the SI unit m/s. Average velocity is displacement divided by time, while instantaneous velocity describes velocity at a particular moment. Velocity can be positive, negative, or zero depending on the chosen reference direction, and changes in velocity are described by acceleration.