[Physics Class Notes] on Velocity Pdf for Exam

Velocity in physics is defined as a vector measurement of the direction and rate of the motion. To be specific, the velocity of an object can also be defined as the rate of change in the object’s position corresponding to a frame of reference and time. In simple words, the term velocity gives us an idea of the speed at which an object is moving in a particular direction. It is what tells how slow or fast something is moving. Let’s take an example where two objects are moving. Identifying which of the two objects is moving faster than the other one is easy if they both are moving in the same direction. However, determining the faster object is quite difficult if the two are travelling in opposite directions. Considering such difficulties and thus eliminating them, our scientists came up with the concept of velocity to help the observers in identifying the faster or slower objects with ease. Here, we will be going to discuss this concept in detail. 

What is Velocity?

Velocity is a vector measurement of the rate of motion of an object and the direction in which it is moving. Hence, to determine the velocity as per this definition, we should be familiar with both the magnitude and direction. For instance, if an object travels towards the west at 5 meters per second (m/s), then its velocity will be 5 m/s to the west. A simple formula given below is the most common and easiest way to calculate velocity.  

r = d / t

where,

r is the rate (sometimes denoted as v, representing velocity)

d is the distance the object moved 

t is the time the object took to complete the movement

Units of Velocity

Although the SI unit for velocity is m/s (meter per second), it can be expressed in any unit of d/t (distance per time). Some of the units in which one can express velocity is miles per hour (mph), kilometres per second (km/s), and kilometres per hour (kph).

Initial and Final Velocity

Initial velocity is the speed (along with direction) of the object with which it starts moving. On the other side, the final velocity is the speed (along with direction) of the same moving object once it has reached its final position. 

How to Find the Initial Velocity?

The initial velocity (vi) is the velocity of the object before a change due to acceleration. Hence, it can be calculated by using the below formula:

vi = vf – at

where, 

vi = initial velocity (m/s)

vf = final velocity (m/s)

a = acceleration (m/s²)

t = time between the start and end of the acceleration (s)

How to Find the Final Velocity?

The final velocity of an object is equal to its initial velocity plus acceleration multiplied by the time it travelled, and can be given as:

v = u + aΔt

where, 

v = final velocity

u = initial velocity

a = acceleration 

t = time 

As the equation shows; for a given object, you can calculate its final velocity by adding its initial velocity to the acceleration due to force multiplied by the time for which the force applied to it. The delta (Δ) in front of the time (t) displays the change in time, which can be written as tv − tu. Here, tv – tu is the time elapsed from u to v.

Speed and Velocity

Most of us often get confused by the terms speed and velocity, as the concepts of both of these terms revolve around how fast something is moving. Well, although the concepts are a bit similar, these terms are quite different from each other. The main difference between speed and velocity is that speed gives an idea of how fast the body is moving, whereas velocity not only gives the idea of the body’s speed but also tells the direction in which it is moving. Speed is related to distance travelled, whereas velocity is to displacement. Average velocity, which is the total displacement by total time, is always either less than or equal to the average speed. It is so because the displacement can never be more than the distance travelled, whereas the distance travelled can be more than the displacement.    

Difference between Speed and Velocity

The basic difference between speed and velocity is that the former has only magnitude, while velocity has both magnitude and direction. It means the velocity is the speed with direction. 

Other Detailed Differences between Speed and Velocity are as Follows:

Speed is the quantitative measure of how fast a body is moving, whereas velocity measures not just the speed at which the body is moving but also the direction in which it is moving. In other words, speed determines only how fast something is travelling, while velocity determines how fast something is travelling, along with the direction of its movement.  

As the speed emphasizes only the magnitude, it is termed as a scalar quantity. On the other hand, the velocity is a vector quantity as it focuses on both the magnitude and direction. 

Speed is defined as the rate of change of distance, whereas velocity refers to the rate of change of displacement.

The average speed of a moving body can never be zero or negative. But, the velocity of a moving body can undoubtedly be zero.

Speed is distance/ unit time. On the other side, velocity is displacement/ unit time.