Physics of Vectors & Motion Mechanics (7.0 hrs | 63 lessons)
4.2 (23 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
2,783 students enrolled

Physics of Vectors & Motion Mechanics (7.0 hrs | 63 lessons)

Video lessons on mechanics for AP Physics, physics 1, high school physics and physics for IIT JEE
4.2 (23 ratings)
Course Ratings are calculated from individual students’ ratings and a variety of other signals, like age of rating and reliability, to ensure that they reflect course quality fairly and accurately.
2,783 students enrolled
Created by Vishesh Nigam
Last updated 7/2020
English [Auto]
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What you'll learn
  • What are Vectors and Scalars
  • Vector Components and Unit vectors (I,j and k)
  • Dot Product and Cross Product
  • What are Position and Displacement Vectors
  • Velocity, speed and displacement
  • Instantaneous Velocity and Acceleration
  • 3 Equations of motion
  • Area under a velocity -time curve
  • Projectile Motion: Why Vertical Velocity changes, Horizontal does not
  • Projectile Motion: Why a Parabolic Path? Why Max Range at 45 degree
  • Circular Motion: What is Centripetal Force
  • This course assumes you have studied Physics in standard 10 or High School

How can you become really good at topics like Vectors and  mechanics of motion in 1,2 and 3 dimension in physics?

With over 2700 enrollments and 4.7 star rating, these 62 lessons will help and guide you to become good at these topics

This topic covers the concept of mechanics,  vectors, displacement and velocity and acceleration in two and three dimensions. Projectile motion and circular motion is explored in depth. Motion in 2 and 3 Dimension requires use of vectors to describe the motion of the bodies. Vector notation is used in most places to understand and appreciate the close dependence of this kind of motion on vectors.

Like most topics in Physics, this too requires deep understanding of concepts to make sense of numerical problems and their solutions.

Learn physics faster and better - It is not difficult!  It just requires a some time, focus and a good teacher :)

Once you are enrolled in the course, all you need a note book and  a pen to get cracking on these topics

What are Vectors and Scalars

Vector Components and Unit vectors (I,j and k)

Dot Product and Cross Product

What are Position and Displacement Vectors

Velocity, speed and displacement

Instantaneous Velocity and Acceleration

3 Equations of motion

Area under a  velocity -time curve

Projectile Motion: Why Vertical Velocity changes, Horizontal does not

Projectile Motion: Why a Parabolic Path? Why Max Range at 45 degree

Circular Motion: What is Centripetal Force

Whats different about my courses:

When I create content for the lessons, I think deeply around the areas where students struggle and feel confused. My lessons tackle these parts in depth. Also, I believe visual representation of various ideas makes a lot of impact. The lessons have visuals and animations that are thought through quite deeply

And most importantly, I make myself available personally to answer questions that a student who has enrolled may have

My students wrote this to me

Bobbie Smith:                           Amazing explanations, I really learned a lot. Thank you.

Satyam Jha:                               amazing!! i could not understand vectors in my class but here it is very easy to understand Thanks a lot!!

Csaba:                                        I learned new ideas of approaches. I'm looking to try them in my professional practice as a teacher.Thanks! :)

Fernando  P. Radaza:              It help me a lot to understand better about Physics of Work, Power & Energy.

Chamara Dilshan:                    it's good, explaining every small thing ,it's good to start physics beginners

Onofrio :                                   The lessons given by the teacher are very interesting! Excellent course!

Simaran:                                    Very deep understanding of the subject Shiva Very knowledgeable and sounds very nice and helpful

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Pawan Kumar:                         The way to teaching us is amazing with all diagrams

Samit                                          This course has a lot of good content and very well presented. Thank you

Dani:                                            It was concise and consequent. The exercises were good exposed and explained. Simply excellent. I promise,     that i will use some ideas in my every day practice in my classroom. I'm also teaching physics, but in Hingarian. I finished this course to improve my skills, first of all in interesting approaches, and foreign language skills as well. This course was exactly what I expected!

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Who this course is for:
  • Students taking AP Physics, Physics 1, high school physics etc.
  • Students preparing for competitive exams - IIT-JEE, NEET, CBSE etc.
  • Physics Enthusiasts
  • Curious minds in pursuit of "how things work?"
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Course content
Expand all 63 lectures 06:54:39
+ Vectors and Motion in Two and Three Dimension
17 lectures 02:53:22

Vectors form the foundation of several topics in Physics but dealing with them can be confusing. This lesson starts from the basics and builds up on what are vectors and how you add and subtract them. Includes use of unit vectors, cross product, dot product etc.  Vectors are fundamental in the physical sciences. They can be used to represent any quantity that has magnitude, has direction, and which adheres to the rules of vector addition. An example is velocity, the magnitude of which is speed.

Preview 10:39

Understanding vector components or vector resolution and how you can add the components to form vectors is essential to solve higher level problems in various topics of Physics. So vectors can sometimes be very confusing and the best way of dealing with them is to put them in a coordinate system

What are Vector Components?

A unit vector is any vector that has a magnitude of "one". It can point in any direction. Such vectors are usually used to specify directions and therefore they do not have any dimension like other vectors (e.g. m/s for velocity).

The unit vectors in the positive direction of x, y and z axis are labelled as i,j and k respectively with a small hat on top. They are used to express other vectors by combining the magnitudes of those vectors with i,j and k. Example a vector V having magnitude “a” in x direction  and “b” in y direction can be written as V = ai + bj (V needs to have an arrow on top while i and j should have cap as per the proper notation)

What are Unit Vectors i, j and k? What use do they have?

Vector Multiplication usually takes 3 forms - (a) Dot Product (b) Cross product and (c) Vector multiplied by a scalar.

Watch this video for easy understanding of this topic. Multiplication of a vector by a scalar changes the absolute value of  the vector, but the direction remains the same. The scalar value alters the magnitude of the vector. The scalar in a way increases or reduces the vector. The dot product of two vectors is the value of one vector multiplied by the projection of the second onto the first one.

The cross product of two vectors is basically the area of the parallelogram between them in value terms. The symbol used to represent this multiplication is a diagonal cross and that is why it is termed "cross product". This product has value and direction.

Dot Product | Product of Vector with Scalar

Finding Cross Product of 2 vectors and the direction of the resultant vector is easy, provided one understands the simple cork screw rule. In this lesson, find how cross product is calculated and how it differs from dot product.

The cross product of 2 vectors f and g is defined in three-dimensional space only and is expressed as f × g. Cross product a × b is defined as a vector c that is perpendicular to both a and b, and has direction given by the cork screw rule or the right-hand rule and a magnitude is the area of the parallelogram that the vectors make

Preview 06:37

Average velocity, speed and displacement as concepts help us work around motion. "Motion in a straight line" is one of the most interesting topics in Physics. In this tutorial, we will cover the concepts and see how these can be applied to solve some difficult numerical problems     

Velocity, Speed and Displacement

Instantaneous velocity and acceleration as concepts are quite often misunderstood. They require an understanding of basic level calculus. While average velocity is measure over a period of time, instantaneous velocity is measured at an instant in time. In this lesson you will understand what it is and when it is to be used.

What is Instantaneous Velocity and Acceleration?

There are three basic equations of motion that can describe the kinematics of an object very well. This is first of the equation where the acceleration is assumed constant

Equation #1 of Motion : v = u +at

This lesson explores and derives equation number two of motion and also a very useful way of looking at velocity time graphs and how you can calculate displacement using area under the curve.

Equation # 2 of Motion and Area under the curve

This is the third of the 3 equations of motion. With an understanding of these three equation, almost all related numerical can be solved

Equation # 3 of Motion: V(sq) = U(sq) + 2.a.s

Vertical Motion is a unique form of motion in one dimension. Learn how the gravity affects the velocity vector of an object in free fall.

Motion under gravity: Vertical motion

Motion in 2 & 3 Dimension starts with good understanding of what are position and displacement vectors. Once you understand the 2 concepts, it becomes much easier to understand the topic that may include different kind of motions like projectile or circular motion.

Position and Displacement Vectors #1

The concept of instantaneous velocity and acceleration along with average velocity and acceleration is foundation of working around the topic. Learn how the two differ and how you can use each of them to solve numerical problems

Instantaneous Velocity and Acceleration #2

Projectile motion involves velocity in vertical and horizontal direction. It is important to understand that the two are independent of each other. Solving problems becomes much easier with this simple understanding.

Preview 15:29

It is a wonder that Projectile Motion takes a Parabolic Path and 45 degree is the angle that offers maximum range. Study the math behind the physics of the topic. In this video, understand the concept of range and angle of projection for maximum displacement in horizontal direction

Projectile Motion: Why a Parabolic Path? Why Max Range at 45 degrees? #4

Circular Motion involves Centripetal Force and Acceleration that can be difficult to understand. This lesson explains how a center seeking force results in circular motion.

Circular Motion: What is Centripetal Force? #5

This lesson summarizes the different aspects of motion in a straight line or rectilinear motion

Summary - Motion in a straight line
+ Numerical Problems and Solutions (AP Physics, Physics 1, Subject SAT)
46 lectures 04:01:17

The problem has a boatman having a displacement vector that takes him to the wrong destination. It is required to find the vector that takes him to the intended destination. This problem requires us to identify the three vectors i.e. the actual displacement vector, intended displacement vector and the required vector to reach the destination.

Skillful addition of vectors to form the equation helps in solving the problem

Boatman's Displacement Vector

The problem has a vector placed in the 3rd Q. We need to establish the components of the vector. This requires taking the proper angle that the vector makes with the X axis. Vector problems often require beginners to identify the location of the vector and then establish the angle and therefor eventually the sign of the vector components

Find the Vector Components in 3rd Q

Solution to the problem requires conversion of  3 displacement vectors into i,j,k notation and finding the resultant vector by adding them.

Often the vectors are expressed as displacement in meters. Converting them to i,j,k form requires carefully putting them on the cartesian plane and finding the sum

Adding 3 Vectors in i, j, and k Notation

The problem has vector C = sum of vector A and vector B, further magnitude of C = that of vector A. The information is to be used to find vector C FOR ONLINE TUTORIALS BY ME: Please write to Please also indicate (a) Your class (11th, 12th, High School etc.) (b) Preferred time slot for tutorial PDF COPY OF PROBLEM, WRITE TO: MORE PROBLEMS & SOLUTION: SUBSCRIBE TO "THE SCIENCE CUBE": FACEBOOK: The problem requires skillful use of expressing vectors in an equation form to solve for the unknown vector.

If Vector C= Vector A + Vector B, Find C

The problem combines the use of i, j and k vector notation and the parallelogram method to solve the problem. This requires placement of vectors on the coordinate plane and converting the vectors into i,j,k notation and establishing a relationship between them. alternately, the parallelogram method of finding vectors can also be adopted. Finding the right angle that a vector makes with the X axis is also very important

Using i,j and k Vector notation | Parallelogram method

Finding the correct angle that the vector makes with the X axis is very important step in solving vector problems.

Angle of the vector with X axis

How do you find the area of the triangle between two vectors?

Preview 02:16

The problem has 2 footballers making 2 vector moves (displacement). We need to find the 2nd vector move of 2nd player so that they end at the same point

Vectors in the Football field

How to find angle between 2 vectors by using dot product is often asked by students. We make use of the fact that the dot product in the form ab cos (theta) = product expressed in i,j,k notation.

Finding Angle between 2 Vectors using Dot Product

Vector Problems that requires us to find the direction of vector that is a result of cross product of 2 vectors are quite often encountered in Physics. Use this example to understand this better

Direction of Vector Cross Product

A wheel is rolling and after half a roll, the vector position of a point P changes from bottom to top. Find by combining horizontal and vertical vector, the displacement vector

Finding Displacement by Combining Components

The problem requires us to establish 2 vectors in XYZ plane and then find their dot product and cross product. The vectors need to be converted to i,j,k notation to solve the problem

Dot and Cross Product in XYZ Plane

Problem requires us to find a vector, if the angle they make with a known vector is given.The projection of one vector is negative and other positive. Find the vectors

Find the missing Vector

Given a graph that plots the velocity vs. time for a runner, find displacement of the runner

Preview 02:45

The problem brings out the difference between velocity and speed calculation

Average velocity and speed of a car

The problem has displacement x as a function of time t. Using this equation, we are asked to find the average velocity and displacement for various time intervals

Use of displacement time graph to find velocity

A bird flies between 2 cars traveling in opposite direction. What is the distance traveled by the bird till the 2 cars meet

Distance traveled by a bird between cars

The problem has a particle and its position x is given as a function of time.

Description of motion of a particle given d= f(t)

An electron is accelerated between 2 plates. The problem is around how to find acceleration at the exit of the 2nd plate given displacement and velocity at exit

Acceleration of an electron between plates

The problem helps us to understand the displacement of a car moving in a straight line with given certain other time motion data like velocity and time. See how to identify and use the correct equations of Motion

Displacement of a car

This problem shows the position of particle on a displacement time graph. The question is what are the magnitude and direction of acceleration. Learn how two equations of motion help solve the problem

Particle on a graph

What would be the velocity of a packet being carried up by a parachute when it is dropped and hits the ground. Important to understand that the initial velocity vector of the packet would be same as that of the balloon. Therefore use of appropriate sign for velocity as a vector is essential for putting in the equation of motion that is used.

Velocity of a packet from a hot air balloon

What method to use for measuring the time time and velocity in the end 20% displacement of a bolt falling in a valley? Making proper diagrams with all information and identification of correct equations is the key to solving such problems.

Velocity and displacement of a falling bolt

This problem involves a car at a certain speed and acceleration. Should the driver decelerate or speed up to beat the traffic signal turning red? The answer lies in analyzing both situations through equations of motion.

Car speed and acceleration and the traffic signal

The acceleration or deceleration required to avoid collision between 2 trains requires smartly crafting equations of motion and applying them to solve the problem. Learn how to go about such problems.

Acceleration required to avoid accident

The problem has basketball player jumping up with a certain initial velocity. What is the velocity of the player at various displacements and what is the time taken between various Y values

Basketball player: displacement and velocity

What are displacement and velocity of two diamonds, dropped from a building at different times. At what time are they 10 m apart? The problem requires careful plotting of information on a diagram and deriving the equations that connect velocity, time and displacement under gravity to give the solution

Falling diamonds: equations of motion

A parachutist falls under gravity and then the chute opens. What are velocity, displacement at various times. This problem tells us how the direction of acceleration is opposite the direction of fall and positive despite being a deceleration. Also, how the equations of motion are wisely used to solve the problems

Preview 08:58

Particle accelerates, stays at constant velocity and then decelerates. The information is on a velocity- time graph. Infer the time when it is at zero acceleration

Velocity time graph

The problem has 2 particles, one with constant acceleration and other with variable. At what time are the velocities the same? We are required to make smart use of integral and differential calculus to form two equations that can be equated for equal velocity to find the time

Variable acceleration

Given the Projectile Motion of a box dropped from a plane with data on angle of drop, the initial velocity vector and the horizontal displacement of the box, what is the time of flight and the height from which it is dropped.

The Fighter Jet - Projectile Motion of a Bomb #1

Trajectory of a bullet is also parabolic in nature, it is however not noticeable due to high initial velocity. This problem tries to find the angle a bullet should be shot above the horizontal such that the parabolic nature of the trajectory is neutralized and the bullet hits the bulls eye.

Bulls Eye - Projectile Trajectory of Bullet #2

Projectile Motion problems can often be solved by way of "time reverse" motion method. This is a concept better understood by way of a solving a problem. In this example, we have an object thrown from top of a building and it takes a certain trajectory. Given the velocity and angle at which it hits the ground, find the angle of throw and the initial velocity.

Ball from the Building - Range of motion #3

Often students believe that 45 degree throw always gives max horizontal displacement.  Lets examine the nuance of this belief.

The Shot Putter - Angle of projection #4

This problem finds the angle at which an archer fish should spit a water projectile to hit an insect at the max height of the projectile of the spit ball. The angle needs to be more than the straight line angle that the fish makes with the insect.

Preview 05:00
Ball up the Plane and Projectile Angle #6

What is the dot product and cross product if acceleration at an instant is given in vector notation

Dot and Cross Product in Circular Motion #7

This problem finds how you can find 2 angles of projection to get the same range of motion. It makes use of the parabolic equation of motion of a projectile

The Footballer - Kick for a Projectile Range #8

What will be the components of initial velocity if the coordinates of the projectile are given at time t = 2 seconds. As such, the problem wants us to reverse calculate to find the initial velocity

Projection Velocity #9

This problem helps understand how the range and time of flight of a projectile is calculated when it is projected on an inclined plane. The problem helps in analyzing how a different frame of reference can help quickly arrive to the solution

Range on Inclined Plane #10

This problem dwells on how to find center coordinates of circular motion if velocity "v" and centripetal acceleration "a" is given at time "t"

Finding Center of Circular Motion #11

The problem has a particle moving in two dimensional plane. At a certain instant the X coordinate is 29 m. Also, the initial velocity of the particle is given. Find the position vector of the particle

Find Position Vector | Given one coordinate and velocity #13
Displacement & Velocity of a Plane - City A to B #14
Finding Position Vector - 2 Unknown Variables #15

The problem requires us to find at what velocity should mass "m" move to generate centripetal acceleration in the system that in turn brings about equilibrium in the system or the Mass M stays stationary

Find Velocity for Equilibrium #16

Two rats are placed on a disc at radius r1 and r2. If centripetal acceleration of one rat is given, calculate the acceleration of the other

Rats on a Disc | Find Centripetal Acceleration #12