Kinematics One Dimensional Motion Basic and Advanced

Name: Kinematics One Dimensional Motion Basic and Advanced
Rating: 4.3 (3 reviews)

Basic Definitions involving differentiation and integrationwith Equations of Motion and Graphs

Created byKalyan Dutt Shatdarsanam

Last updated 10/2021

English

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What you'll learn

You will understand basic kinematical quantities like distance travelled, displacement, velocity etc by using integrals
You will learn definitions involving differentiation and integration
You will learn equations of motion for constant acceleration
You will learn graphs and solving problems with graphs

Course content

6 sections • 31 lectures • 5h 27m total length

Introduction4:18
Explore one-dimensional kinematics by defining position, displacement, speed, velocity, acceleration, and distance traveled. Use calculus to derive the position-time relation and, from it, determine velocity and acceleration for predicting motion.
Position Vector and Displacement Vector8:46
Define the position vector as the line from origin to a particle, showing dependence on coordinate system, and define the displacement vector as the change in position, independent of coordinates.
How to find Average of a Quantity11:39
Learn how to compute the average of quantities that change over time, using time integrals, for scalar and vector quantities, with applications to speed and velocity.
Velocity and its direction12:40
Define velocity as the rate of change of position, expressed as v = dr/dt. Velocity points along the path tangent, with components along x, y, and z.
Example on finding velocity from position5:59
Speed and intricacies in its definition7:46
Explore how speed equals the magnitude of velocity and also the rate of change of distance traveled, and how displacement versus distance traveled relate in infinitesimal limits.
Displacement and Distance Travelled from Velocity and Speed6:25
Displacement is velocity integrated over time, not velocity multiplied by time unless velocity is constant. Distance traveled is speed integrated over time, and we treat x, y, z components separately.
Average Speed and Average Velocity5:21
Calculate average speed as distance traveled divided by time and average velocity as displacement divided by time, with circular motion illustrating their difference and constant velocity yielding equality.
Definition and Direction of Acceleration10:08
Acceleration is the rate of change of velocity, caused by a nonzero net force, and points in the direction of that net force.

Special case of Constant Acceleration10:59
Derive the velocity time relation for constant acceleration via a differential equation and integration, yielding velocity equals initial velocity plus acceleration times time, and decompose the vector into independent directions.
The first two equations of motion9:47
Derives the two equations of motion for constant acceleration: v = u + a t and s = u t + 1/2 a t^2, via integration, clarifying displacement vs distance.
The third and fourth equations of motion14:50
Derives the third and fourth equations of motion for constant acceleration, including v^2 = u^2 + 2 a s and s = (u+v)/2 t.
The only scalar equation of motion8:52
derive the scalar equation of motion for constant acceleration: v^2 = u^2 + 2 a s, by dotting the velocity equation with itself.

One Dimensional Kinematics Definitions10:35
Define one-dimensional rectilinear motion along the x axis, with position x, velocity along x, and acceleration along x. Derive constant-acceleration equations and key relationships between velocity, position, and time.
Different Possible Problems in One Dimensional Kinematics12:03
Examine common one-dimensional kinematics problems, deriving position-time relationships from velocity-time or acceleration-time data, and solving cases via integration across velocity, acceleration, and position relations.

Problem with Velocity vs Time relation given13:14
Explain one-dimensional motion with velocity that changes linearly over time, derive position as x = 4t - t^2, identify constant acceleration, and distinguish displacement from distance traveled.
A beautiful problem on finding distance travelled in rectilinear motion13:10
Explore how to compute distance travelled in rectilinear motion by analyzing velocity zeros, turning points, and piecewise displacements, then generalize to higher dimensions for future problems.
Problems on Acceleration vs Time and Velocity vs Position9:40
Explore solving one-dimensional motion with nonconstant acceleration by deriving velocity-time and position-time relations from integration and differential equations, starting from rest at the origin.
Problem on Acceleration vs Velocity relation9:34
Analyze how velocity changes with time from a specific acceleration-velocity relation, derive the position and total distance traveled, and identify the terminal velocity in a one-dimensional motion scenario.
Problem on Acceleration vs Position Relation (Encountered in Oscillations)9:22
Explain the acceleration–position relation a = -4x in a simple harmonic motion scenario. From x(0)=6, v(0)=0, derive x(t) = 6 cos 2t and v(t) = -12 sin 2t, showing oscillation between -6 and 6.
Minimum distance between police and thief12:08
Explore a one-dimensional pursuit where a police car at 5 m/s cannot catch an accelerating thief, and determine the minimum separation of 50 meters at 20 seconds.
A Tricky Problem on Retarding Car10:44
This lecture solves a one-dimensional motion problem: a locomotive at 54 km/h brakes at -0.3 m/s^2 from 400 m, stops in 50 s, leaving 25 m from the signal.
A Helicopter Problem11:00
Calculate the helicopter's velocity at engine-off by using vertical acceleration 3 m/s^2, displacement, and the last sound travel time to the observer.
A Problem of Acceleration Reversal9:04
Explore a one-dimensional motion problem with zero initial velocity and acceleration reversal, and determine the time to return to start using kinematics from a to b and b to c.

Motion Under Gravity13:31
Explore motion under gravity by analyzing a ball thrown upward and returning to ground, using downward as positive, and applying constant-acceleration kinematics to find time of flight and maximum height.
Three problems on motion under gravity12:31
Explore three problems on motion under gravity, including two planets with different accelerations, analysis of fall times and velocities, and vertical projection scenarios using basic equations of motion.
Problem on motion inside an elevator11:59
Explore one-dimensional motion inside a rising elevator, solving for the bolt's upward motion, its fall under gravity, and the time to hit the elevator floor.
A Problem of Stone thrown from top of wall upwards10:24
This one-dimensional kinematics lecture analyzes a stone thrown upward at 5 m/s from a 30 m wall, landing in 3 seconds under 10 m/s^2 downward, using a whole-motion method.

Graphs in 1-D motion Introduction14:48
Explore one-dimensional motion with velocity-time and position-time graphs. Learn how slope and area under graphs reveal velocity, acceleration, displacement, and distance traveled.
Basic Problems in Graphs10:46
Learn to read velocity-time and position-time graphs, using slope for velocity and acceleration, and area under the curve for displacement and distance traveled.
Problems which can be solved with Velocity vs Time Graph15:56
Explore solving one-dimensional motion problems using velocity-time graphs, including acceleration, constant velocity, deceleration, and computing displacement from the area under the graph.

Requirements

Requires you to know Vectors , Differential and Integral Calculus

Description

Note: This course is intended for purchase by adults (above 18 years) or by parents or guardians of students of age below 18

Here you will be introduced to basic definitions of kinematics involving integration which are as follows: distance travelled, displacement, position vector, average speed, average velocity, speed, velocity and acceleration. Each definition is presented very carefully with proper illustrations and examples. This is followed by a discussion on the special case which one often encounters in kinematics namely the case of constant acceleration.. The equations of motion for this case of constant acceleration are derived and their intricacies are thoroughly discussed. This is followed by a discussion on one dimensional kinematics and the types of problems one encounters in them. The focus of this course is mainly on one dimensional kinematics though the definitions are given keeping in view the two and three dimensional kinematics so that at a later stage you can smoothly transition to two dimensional and three dimensional kinematics. The different problems discussed here cover almost all important cases like velocity-time, acceleration-time, velocity-position, acceleration-velocity and acceleration-position relations and questions after giving these relations. I have extensively used vectors and Calculus and I suggest to go through my vectors and differential calculus and integral calculus courses before venturing in to this topic. Special emphasis is given on graphs and graph based problems. The concepts of calculus like "derivative gives slope" and "integration gives area" are used extensively in the discussion on graphs and their problems. After this course you will have basically mastered almost the whole of one dimensional kinematics and ready to take up two dimensional and three dimensional motion

Who this course is for:

For any adult whose is interested in calculus based physics
For parents whose children are below 18 years and preparing for competitive exams like IITJEE or NEET

Kinematics One Dimensional Motion Basic and Advanced

What you'll learn

Explore related topics

Course content

Introduction9 lectures • 1hr 13min

Constant Acceleration and Equations of Motion4 lectures • 44min

One Dimensional Kinematics Definitions2 lectures • 23min

Problems of One dimensional Kinematics9 lectures • 1hr 38min

Motion under gravity4 lectures • 48min

Graphs3 lectures • 42min

Requirements

Description

Who this course is for: