Overview of Dynamics in JEE Maths

Dynamics is a branch of mechanics that studies the motion of objects and the forces causing this motion. Unlike statics, which deals with objects at rest, dynamics focuses on moving objects and includes concepts like velocity, acceleration, Newton’s laws of motion, and projectile motion. In JEE Maths, dynamics is essential for solving mechanics problems in both JEE Main and Advanced exams.

Direct Links to Download 2025-26 JEE Maths Notes (PDF)

► Click “Download Here” next to your access the free PDF.

♦ Set Theory and Relations ⇒ Download Here

♦ Function ⇒ Download Here

♦ Differentiation ⇒ Download Here

♦ Application of Derivatives ⇒ Download Here

♦ Indefinite Integral ⇒ Download Here

♦ Definite Integral ⇒ Download Here

♦ Area Under Curve ⇒ Download Here

♦ Differential Equations ⇒ Download Here

♦ Vector Algebra ⇒ Download Here

♦ 3D Dimensional ⇒ Download Here

♦ Determinants ⇒ Download Here

♦ Binary ⇒ Download Here

♦ Logarithm  ⇒ Download Here

♦ Complex Number ⇒ Download Here

♦ Progression ⇒ Download Here

♦ Quadratic Equation ⇒ Download Here

♦ Permutations and Combinations ⇒ Download Here

♦ Binomial Theorem ⇒ Download Here

♦ Exponential ⇒ Download Here

♦ Rectangular Cartesian Co-ordinates ⇒ Download Here

♦ Straight Lines ⇒ Download Here

♦ Pair Of Straight Line ⇒ Download Here

♦ Circle System  ⇒ Download Here

♦ Conic Sections ⇒ Download Here

♦ Trigonomerical Ratio ⇒ Download Here

♦ Trigonomerical Equation ⇒ Download Here

♦ Trigonomerical Properties ⇒ Download Here

♦ Height & Distances ⇒ Download Here

♦ Trigonomerical Inverse of Triangle ⇒ Download Here

♦ Hyperbolic Functions  ⇒ Download Here

♦ Probability ⇒ Download Here

♦ Statistics ⇒ Download Here

♦ Statics  ⇒ Download Here

♦ Dynamics ⇒ Download Here

♦ Numerical Method ⇒ Download Here

♦ Linear Programming ⇒ Download Here

♦ Maths Formula PDF for Entrance Exam ⇒ Download Here

Basic Concepts of Dynamics

• Displacement: The change in position of an object.

• Velocity: Rate of change of displacement with respect to time.

  • Formula: v = ds/dt

• Acceleration: Rate of change of velocity with respect to time.

  • Formula: a = dv/dt

• Force: An interaction causing change in motion (Newton’s laws).

• Mass: Quantity of matter in an object, usually denoted by m.

Newton’s Laws of Motion

1. First Law (Law of Inertia): An object continues in its state of rest or uniform motion unless acted upon by a net force.

2. Second Law: Force is proportional to the product of mass and acceleration:

   • Formula: F = ma

3. Third Law: For every action, there is an equal and opposite reaction.

Example: A 5 kg block is acted upon by a 20 N force → Acceleration a = F/m = 20/5 = 4 m/s²

Equations of Motion (Kinematics)

For uniform acceleration:

1. v = u + at

2. s = ut + ½ at²

3. v² = u² + 2as

Example: A car accelerates from rest at 2 m/s² for 5 s → Final velocity v = u + at = 0 + 2×5 = 10 m/s

Projectile Motion

• Motion of an object thrown at an angle to the horizontal.

• Horizontal motion: x = u cos θ · t

• Vertical motion: y = u sin θ · t – ½ gt²

• Maximum height: H = (u² sin² θ)/(2g)

• Range: R = (u² sin 2θ)/g

Example: A ball is projected with u = 20 m/s at θ = 30° → Range R = (400 × sin 60)/10 ≈ 34.64 m

Centripetal and Circular Motion

• Centripetal acceleration: a_c = v²/r

• Centripetal force: F_c = mv²/r

• Objects moving in a circle experience a force toward the center.

Example: Car of mass 1000 kg moving at 20 m/s in circle of radius 50 m → F_c = (1000 × 400)/50 = 8000 N

Work, Energy, and Power in Dynamics

• Work done: W = F · s · cos θ

• Kinetic energy: KE = ½ mv²

• Potential energy: PE = mgh

• Power: P = Work/Time = F · v

Example: Force 10 N moves a block 5 m → Work = 10 × 5 = 50 J

Simple Examples in Dynamics

1. A 2 kg object accelerates at 3 m/s² → F = 2 × 3 = 6 N

2. A ball thrown at 15 m/s at 45° → Max height H = (15² sin²45)/2g ≈ 5.7 m

3. A 10 kg block slides on frictionless surface → F = ma, find acceleration for F = 50 N → a = 50/10 = 5 m/s²

4. A car moves in circular path of radius 20 m at 10 m/s → Centripetal force F_c = (m v²)/r = (1000 × 100)/20 = 5000 N

Applications in JEE Exams

• Motion problems on inclined planes

• Projectile motion questions

• Circular motion and centripetal force problems

• Problems involving work, energy, and power

• Force and acceleration calculations using Newton’s laws

Tips for JEE Exam Preparation

• Memorize kinematics formulas and Newton’s laws

• Draw diagrams for visual understanding

• Solve previous years’ JEE questions for dynamics

• Apply concepts to both 1D and 2D motion problems

• Practice derivations of projectile motion, circular motion, and energy formulas

Conclusion

Dynamics is a crucial part of JEE Maths, covering motion, velocity, acceleration, forces, projectile motion, circular motion, and energy. Mastery of dynamics allows students to solve mechanics problems efficiently in exams. StudentBro.in provides step-by-step explanations, solved examples, and practice problems to help JEE aspirants achieve high accuracy and speed in dynamic-related questions.