Equation of Motion by Calculus Method

Calculus plays a vital role in motion analysis by enabling the derivation of Newton’s equations of motion. Additionally, it provides the means to address scenarios of variable accelerations or variable velocity. Calculus allows Newton’s equations to be used for non-linear motion or variable acceleration.

Equation of Motion by Calculus Method

In Physics, Motion is the state of body in which it changes its position with time. Motion is fundamentally described by physical quantities such distance, displacement, speed, velocity, acceleration, and time. These physical quantities can be expressed in the form of a mathematical equation to express motion. These equations are called Equations of Motion. These equations can be derived via various methods such as Algebraic Method, Graphical Method and Calculus Method.

This article deals with the equation of motion and its derivation using the calculus method. This derivation is useful for class 11 students.

Table of Content

  • Fundamentals of Motion
  • Equations of Motion by Calculus Method
  • Applications of Calculus in Motion
  • Examples on Equation of Motion by Calculus Method
  • Practice Problems on Equation of Motion by Calculus Method
  • Conclusion: Equation of Motion by Calculus Method

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Fundamentals of Motion

The fundamentals of motion in physics are described by the concepts: of distance, displacement, speed, velocity, acceleration, and time. Here’s a brief overview:...

Equations of Motion by Calculus Method

There are three equations of motions also called Newton’s Equation of Motion. The expression of the three equations of motions are:...

Applications of Calculus in Motion

Here are some applications of calculus in motion:...

Examples on Equation of Motion by Calculus Method

Example 1: A body moving along the x-axis has its position given by x(t)=t3-2t+1. Find its velocity and acceleration as a function of time....

Practice Problems on Equation of Motion by Calculus Method

Q1. A car moves along a straight road with its position given by s(t)=2t2-5t+3, where s is in metres and t is in seconds. Determine the car’s velocity and acceleration at time t =3s....

Conclusion: Equation of Motion by Calculus Method

Calculus plays a vital role in motion analysis by enabling the derivation of Newton’s equations of motion. Additionally, it provides the means to address scenarios of variable accelerations or variable velocity. Calculus allows Newton’s equations to be used for non-linear motion or variable acceleration....

FAQs on Equation of Motion by Calculus Method

How many Equations of Motion are there?...