Instantaneous Speed and Velocity

Velocity and Speed are related to Displacement and Distance respectively. Speed is the Distance per unit Time and Velocity is the Displacement per unit Time. Speed has magnitude but no direction i.e. scalar similar to Distance. Velocity has magnitude with direction i.e. vector similar to Displacement.

Formulas for Speed and Velocity:

Speed = rate of change of Distance = \[\frac{\textrm{Change in Distance}}{\textrm{Change in Time}}\]

Velocity = rate of change of Displacement = \[\frac{\textrm{Change in Displacement}}{\textrm{Change on Time}}\]

Similar to Distance and Displacement which have distinctly different meanings regardless of their similarities, Speed and Velocity also have different meanings. A body/ object that moves with a high Speed can cover a large Distance within a short period of Time. Contrast to that will be the Distance covered and Time taken for an object/ body that moves with low Speed. An object with no movement will have a zero Speed.

For instance, a person who is moving rapidly- one step forward and one step backward, it means that he returns to his starting position. This will result in a zero Velocity. The motion will never result in a change of position since the person always tends to return to his original starting point. In order to maximize the Velocity, a person in motion must maximize the Distance that he is displaced from the original position.

Average Speed and average Velocity:

A moving body/ object often undergoes changes. Average Speed is the Distance traveled by the object divided by the Time taken for the travel.

Average speed = \[\frac{\textrm{Distance Traveled}}{\textrm{Time of Travel}}\]

Whereas, average velocity is the changes in the position i.e. the displacement divided by the time taken.

Average velocity = \[\frac{\textrm{Displacement}}{\textrm{Time taken}}\]

Difference between Average Velocity and Average Speed:

Instantaneous Speed:

The rate of change of position with Time is called Speed. As an object moves, its Speed may change accordingly. The Speed of an object at any given instant is called an Instantaneous Speed. It can be determined by finding out the average Speed over a very short Distance and Time.

The formula for Instantaneous Speed:

It is equal to the Speed at an interval of Time. Following is the formula for finding out the Instantaneous Speed:

Instantaneous Speed = limit as a change in Time approaches zero (change in positron/ change in Time)

\[V=lim_{\Delta t\rightarrow 0}=\frac{\Delta _x}{\Delta _t}=\frac{\Delta _x}{\Delta _t}\]

Here, x is the Distance traveled by the body. The Instantaneous Speed is measured in meter per second (m/ s) as it is the Speed at a particular Time interval.

Both the Instantaneous Speed and Velocity will be present in a moving object. The Distance traveled with respect to Time is the scalar quantity and how fast an object is moved is shown by this.

For Example:

A school bus undergoes changes in Speed. Speedometer will show the changes in Speed for a regular interval of Time.

Speed for various objects is given below:

Difference Between Average Speed and Instantaneous Speed:

Instantaneous Velocity:

Velocity at a specific instant in Time is the Instantaneous Velocity. If the Velocity is not constant, then it will differ from that of the average Velocity. At the same Time, for an object with standard Velocity over a period of Time, its Instantaneous Velocity and average Velocity will be the same. The calculation for Instantaneous Velocity at a particular moment is done by substituting the corresponding Time value of a variable, in the first-Time derivative of the Displacement equation.

   Instantaneous velocity=\[V=lim_{\Delta t\rightarrow 0}=\frac{\Delta _s}{\Delta _t}=\frac{\Delta _s}{\Delta _t}\]

Where dS is the Displacement vector.

Difference Between Average Velocity and Instantaneous Velocity:

QUICK HACKS TO MASTER THIS CHAPTER–

• Remember the formulas of average Speed and Velocity. 

To solve the sums related to Speed and Velocity, a student must remember the formulas. The students must write the formulas and then practice the calculations in order to solve the sums with ease. 

Avg Velocity = \[\frac{\textrm{Displacement}}{\textrm{Time Travel}}\].

Avg Speed = \[\frac{\textrm{Distance}}{\textrm{Time}}\]. 

• Solve as many physics problems as required 

Lack of practice can cause a student to forget the fundamental concepts of this chapter. Instantaneous Speed and Velocity has sums on average Speed and Velocity so in order to avoid confusion between the two, a student must solve the calculations.

• Solve the questions from the textbook 

Students are expected to be well versed with the questions present in the textbook in the back of the chapter. It has questions that give out a general idea in regards to the questions that are beneficial for the board Exams or any Exams at all. Solving the calculations regularly will build the foundation for understanding and learning Instantaneous Speed and Velocity.  

•  Understanding the solved Examples in the book

The solved Examples in the textbooks will definitely help a student in getting ready for tougher questions. It is essential in clearing the basic concepts and reading through the Instantaneous Speed and Velocity. Solved Examples are a great way to grasp the topic and know how the sums are solved. So it will save a lot of Time if students practice them immediately after learning the chapter. 

• Clear doubts if there are any 

Instantaneous Speed and Velocity can be hard to understand so it is okay to get stuck here and there in the chapter. Reaching out to the Teachers, friends or using online platforms can help in clearing the doubts and understanding Instantaneous Speed and Velocity quickly and easily. Physics is always essential to be understood instead of simply memorized. Students perform more effectively if they are confident and with less doubts.   

• Solving papers

It is highly recommended for the students to solve the sample papers as well as practice papers regularly for honing their skills in calculating the questions faster. Sample question papers give an overall idea regarding the possible questions which will make the student get used to Instantaneous Speed and Velocity and help during the Exams. Practice papers are awesome if the students are willing to practice and sharpen their knowledge and put it to a better test. 

• Join the online classes for tutoring

Online platforms to get classes are a good way for getting better knowledge regarding Instantaneous Speed and Velocity. This chapter is very essential for physics and it should be taken seriously and understood thoroughly. Students must be willing to learn and expand their knowledge regarding Instantaneous Speed and Velocity. 

• Make notes on the chapter

Taking notes in class and after understanding the chapter is a habit that can help students immensely and it can be useful for the students to understand not only the theory of the chapter but also the practical aspect of it. Fundamental concepts require thorough understanding and writing something down always aids in registering the knowledge. It can also be beneficial while reading before the Exams. 

• Study everyday to stay in touch

Students should study the chapter everyday in order to stay in touch with the chapter, Instantaneous Speed and Velocity. The concepts are vast but very basic that will help the students during the Exams. Reading is a habit that not only helps in deciphering the topics but also honing a skill of quick reads saves Time during Exams. It will acquaint the students with the chapter and they can know where they lack and which parts are their strengths in a particular chapter of the subject. 

The sample papers, practice papers for Instantaneous Speed and Velocity online classes and doubt clearing sessions for the same are available on Vedantu’s official website and mobile application. The solutions can be downloaded from the website as well. It will surely help the students during the Examination season. The students should also consider solving questions from popular books like HC Verma and the solutions to the questions present in the textbook is found on Vedantu regarding the chapter on Instantaneous Speed and Velocity that can be downloaded in PDF formats with ease.