Formula Sheet: Motion in a Plane (2D Kinematics)

In this post, we will learn the Class 11 Chapter 3 Motion in a Plane formula sheet. The Motion in a Plane formula sheet covers everything from Projectile Motion equations to Uniform Circular Motion and Vector Addition tricks. Whether you are preparing for Class 11 exams or competitive tests like JEE and NEET, these formulas and shortcuts will help you solve complex 2D motion problems with ease.

Motion in a plane class 11 formula sheet

Table of Contents

List of All Motion in a Plane Formulas

1. Vector Fundamentals

Position Vector:

r = x\hat{i} + y\hat{j}

Displacement:

\delta r = (x_2 – x_1)\hat{i} + (Y_2 – Y_1) \hat{j}

Magnitude of Resultant Vector:

R = \sqrt{A^2 + B^2 + 2ABcos\theta}

Direction of Resultant (alpha):

tan\:\alpha = \frac{Bsin\theta}{A + Bcos\theta}

Dot Product:

A.B = ABcos\theta (Result\:is\;Scaler)

Cross Product:

|A\times{B}| = ABSin\theta

Average Acceleration:

a_{avg} = \frac{\Delta{v}}{\Delta{t}}= \frac{v_x\hat{i}+v_y\hat{j}}{t}

2. Projectile Motion (The Most Important Part)

Time of Flight (T):

T= \frac{2usin\theta}{g}

Maximum Height(H):

H = \frac{u^2sin^2\theta}{2g}

Horizontal Range (R):

R = \frac{u^2sin2\theta}{g}

Trick: If the range is maximum, then Theta = 45 °

R = \frac{u^2}{g}

Equation of Tragectory Path:

y = xtan\theta-\frac{gx^2}{2u^2cos^2\theta}

Velocity at any time t:

v = \sqrt{(ucos\theta)^2+(usin\theta-gt^2)}

Radius of Curvature at the top of the Projectile’s Path:

\rho = \frac{u^2cos\theta}{g}

3. Horizontal Projectile (From a Height h)

Time to hit the Ground:

t = \sqrt{\frac{2h}{g}}

Horizontal Range:

R=u\sqrt{\frac{2h}{g}}

Velocity on Impact:

v = \sqrt{u^2+2gh}

4. Uniform Circular Motion

Angular Displacement:

\Delta\theta = \frac{\Delta{s}}{r}

Angular Velocity:

\omega = \frac{2\pi}{T}

\omega = 2\pi{f}

Relation Between Linear and Angular Velocity:

v = r\omega

Centripetal Acceleration:

a_c = \frac{v^2}{r} = \omega^2r

Total Acceleration (non-uniform):

a_{total} = \sqrt{a_c^2 +a_t^2}

5. Relative Motion in 2D

General Formula:

V_{AB} = V_A -V_{B}

Rain-Man Problem:

To protect himself from rain falling vertically at v_r, a man walking at v_mmust hold his umbrella at anangle theta:

tan\theta=\frac{V_m}{v_r}

River Boat Problem:

To cross a river of width (w) straight across, the boat must head at an angle:

sin\theta = \frac{V_{river}}{V_{boat}}

Shortest time to cross a River:

t_{min} = \frac{\omega}{V_{boat}}

Variables & Symbols Used in Formulas

Symbol	Discription
r	Position Vector
R	Resultant Vector/Horizontal Range
θ	Angle of Projection
α	Direction of Resultant Angle
u	Initial Velocity
v	Final Velocity
ω	Angular velocity (omega)
T	Total Time of Flight
H	Maximum Height

Formula Sheet: Motion in a Plane (2D Kinematics)

List of All Motion in a Plane Formulas

1. Vector Fundamentals

2. Projectile Motion (The Most Important Part)

3. Horizontal Projectile (From a Height h)

4. Uniform Circular Motion

5. Relative Motion in 2D

Variables & Symbols Used in Formulas

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