Circular Motion Calculator: Circular Velocity and Centripetal Acceleration

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Circular Motion
Calculator

Calculate Circular Velocity and Centripetal Acceleration easily. Enter your values and get instant step-by-step solutions.

🔵 Circular Velocity (v) ⚡ Centripetal Acceleration (a) 📋 Step-by-Step

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Circular Velocity

Find the speed of an object moving in a circular path

✅ Result

—

Step-by-Step Solution

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Circular Velocity (v)

The speed of an object moving along a circular path. It depends on the radius and the time taken to complete one full revolution.

v = 2πr / T

Also written as: v = ωr

⚡

Centripetal Acceleration (a)

The acceleration always pointing toward the center of the circle. It keeps the object moving in a circular path instead of a straight line.

a = v² / r

Also written as: a = ω²r

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Key Facts

Important things to remember about circular motion

1

Even at constant speed, circular motion has acceleration — because direction keeps changing.

2

Centripetal acceleration always points toward the center of the circle — never outward.

3

The force causing centripetal acceleration is called Centripetal Force: F = mv²/r

4

Angular velocity: ω = 2π/T — relates to how fast the angle changes per second.

5

One full revolution = 2π radians. Period T is the time for one complete circle.

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Variables & Symbols

All symbols used in circular motion formulas

Symbol	Meaning	Unit	Description
v	Circular Velocity	m/s	Speed along the circular path
r	Radius	m	Distance from center to object
T	Time Period	s	Time for one full revolution
a	Centripetal Acceleration	m/s²	Acceleration toward center
ω	Angular Velocity	rad/s	Rate of change of angle
f	Frequency	Hz	Revolutions per second (f = 1/T)
π	Pi	—	≈ 3.14159
F	Centripetal Force	N	F = mv²/r (needs mass m)

March 30, 2026

Projectile Motion Calculator : Projectile range, Projectile Max height and Time of flight

AI-Powered Physics Engine

Projectile Motion
Calculator

Calculate Range, Maximum Height & Time of Flight instantly. Enter launch velocity and angle — get all three results with step-by-step solutions.

🎯 Range (R) 📐 Max Height (H) ⏱️ Time of Flight (T) 📋 Step-by-Step 📚 NCERT Based

🚀

Complete Analysis

R, H & T Together

Calculate all three values
at once from u and θ

🔍

Find Unknown

Solve for u or θ

Given R, H or T —
find velocity or angle

📐

Angle Optimizer

Max Range Angle

Find optimal angle
for maximum range

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Complete Projectile Analysis

Enter initial velocity and launch angle to get R, H and T

✅ Results

Projectile Motion

Step-by-Step Solution

🎯

Range (R)

Horizontal distance covered by the projectile from launch to landing point on same level.

R = u²sin(2θ) / g

📐

Maximum Height (H)

The highest vertical point reached by the projectile above the launch point.

H = u²sin²(θ) / 2g

⏱️

Time of Flight (T)

Total time the projectile remains in the air from launch until it returns to same height.

T = 2u·sin(θ) / g

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Key Concepts

Important facts about projectile motion

1

Projectile motion = horizontal (uniform) + vertical (uniformly accelerated) motion combined.

2

Maximum range occurs at θ = 45°. At this angle, sin(2θ) = sin(90°) = 1 (maximum).

3

Complementary angles give the same range: e.g., 30° and 60° produce equal R.

4

At maximum height, vertical velocity = 0. Only horizontal component remains.

5

Air resistance is neglected. Gravity g = 9.8 m/s² (use 10 for NCERT approximation).

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Variables & Symbols

All symbols used in projectile motion

Symbol	Quantity	SI Unit	Formula Role
u	Initial Velocity	m/s	Launch speed
θ	Launch Angle	degrees (°)	Angle with horizontal
g	Gravity	9.8 m/s²	Downward acceleration
R	Range	m	Horizontal distance
H	Max Height	m	Peak vertical height
T	Time of Flight	s	Total air time
ux	Horizontal Component	m/s	u·cos(θ)
uy	Vertical Component	m/s	u·sin(θ)

March 30, 2026

Equation of Motion Calculator – 1st, 2nd & 3rd Equation Solver

AI-Powered Physics Engine

Equations of Motion
Calculator

Solve all three equations of motion with step-by-step AI solutions. Enter any known values and instantly find the unknown.

⚡ 1st Equation 📐 2nd Equation 🔮 3rd Equation 📋 Step-by-Step 📚 NCERT Based

🎯

1st Equation: v = u + at

Solve for: final velocity, initial velocity, acceleration, or time

Solve For

⚠️ Please enter valid numbers in all required fields!

✅ Result

v = u + at

FINAL VELOCITY

—

m/s

Step-by-Step Solution

⚡

1st Equation of Motion

Relates final velocity to initial velocity, acceleration and time. Used when displacement is not required.

v = u + at

📐

2nd Equation of Motion

Gives displacement in terms of initial velocity, time and acceleration. Derived by integrating velocity.

s = ut + ½at²

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3rd Equation of Motion

Connects velocity and displacement without time. Most useful in projectile & free-fall problems.

v² = u² + 2as

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Derivation Summary

How each equation is derived

1

From definition of acceleration: a = (v−u)/t → rearranging gives v = u + at

2

Average velocity = (u+v)/2. Displacement = avg velocity × time → s = ut + ½at²

3

Eliminate t from 1st & 2nd equations → v² = u² + 2as (time-independent equation)

⚠️

All three equations are valid only for uniform acceleration (constant a) in a straight line.

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Variables & Symbols

All symbols used in equations of motion

Symbol	Quantity	SI Unit	Type	Notes
v	Final Velocity	m/s	Vector	Velocity at end of motion
u	Initial Velocity	m/s	Vector	Velocity at start of motion
a	Acceleration	m/s²	Vector	Must be constant (uniform)
t	Time	s	Scalar	Duration of motion
s	Displacement	m	Vector	Straight-line distance
g	Gravity	9.81 m/s²	Vector	Use 10 m/s² for NCERT

March 29, 2026

Acceleration Calculator – Solve All Equations of Motion Instantly

🚀

Acceleration Calculator

Master Newton’s Laws with our interactive acceleration calculator. Solve for acceleration, velocity change, or time instantly with step-by-step solutions!

📐 Kinematics ⚡ Instant Results 📋 Step-by-Step 📚 NCERT Based

📌 Core Formula

a = (v − u) ÷ t

FIND ACCELERATION

a = (v − u) / t

FIND FINAL VELOCITY

v = u + at

FIND INITIAL VELOCITY

u = v − at

FIND TIME

t = (v − u) / a

🎯

Choose What to Solve

Select a mode and enter your known values

⚡ Final Velocity (v)

⚡ m/s

🔙 Initial Velocity (u)

🔙 m/s

⏱️ Time (t)

⏱️ s

🔙 Initial Velocity (u)

🔙 m/s

🚀 Acceleration (a)

🚀 m/s²

⏱️ Time (t)

⏱️ s

⚡ Final Velocity (v)

⚡ m/s

🚀 Acceleration (a)

🚀 m/s²

⏱️ Time (t)

⏱️ s

⚡ Final Velocity (v)

⚡ m/s

🔙 Initial Velocity (u)

🔙 m/s

🚀 Acceleration (a)

🚀 m/s²

⚖️ Mass (m)

⚖️ kg

🚀 Acceleration (a)

🚀 m/s²

🔙 Initial Velocity (u)

🔙 m/s

🚀 Acceleration (a)

🚀 m/s²

⏱️ Time (t)

⏱️ s

⚠️ Please enter valid numbers in all fields!

✅ Result

—

📋 Step-by-Step Solution

🚀

What is Acceleration?

Acceleration is a vector quantity that describes the rate of change of velocity with respect to time. It can be a change in speed, direction, or both.

a = (v − u) / t

📊

Average Acceleration

Average acceleration is the total change in velocity divided by total time. It tells us how fast velocity changed over an interval.

a_avg = Δv / Δt

⚡

Instantaneous Acceleration

Acceleration at a specific instant in time. It is the second derivative of position or the first derivative of velocity with respect to time.

a = dv/dt = d²x/dt²

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SI Unit & Dimensions

The standard unit of acceleration is metre per second squared (m/s²). Its dimensional formula is [M⁰ L¹ T⁻²].

[M⁰ L¹ T⁻²]

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Newton’s Second Law

Force equals mass times acceleration: F = ma. A net force on an object causes it to accelerate in the direction of the force. More mass = less acceleration for same force.

F = m × a

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Gravitational Acceleration

On Earth’s surface, all objects fall with the same acceleration due to gravity: g = 9.81 m/s² (approx. 10 m/s² in NCERT). This is independent of mass.

g = 9.81 m/s²

🗂️

Types of Acceleration

UniformConstant acceleration in a straight line

Non-UniformChanging rate of velocity change

PositiveVelocity increasing with time

Negative (Decel.)Velocity decreasing (retardation)

CentripetalDirected toward center of circular path

GravitationalDue to Earth’s gravity (9.81 m/s²)

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Variables & Symbols

All mathematical symbols used in acceleration formulas

Symbol	Quantity	SI Unit	Type
a	Acceleration	m/s²	Vector
v	Final Velocity	m/s	Vector
u	Initial Velocity	m/s	Vector
t	Time	seconds (s)	Scalar
s	Displacement	m	Vector
F	Force	Newton (N)	Vector
m	Mass	kilogram (kg)	Scalar
g	Gravitational Accel.	9.81 m/s²	Vector

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Key Acceleration Equations

All important formulas — Equations of Motion

Basic Acceleration

a = (v−u) / t

1st Equation of Motion

v = u + at

2nd Equation of Motion

s = ut + ½at²

3rd Equation of Motion

v² = u² + 2as

Newton’s 2nd Law

F = m × a

Centripetal Accel.

a = v² / r

Free Fall

a = g = 9.81 m/s²

Average Accel.

a = Δv / Δt

🚀 IrfanEdu.com

Free Physics Calculators for Students & Educators
irfanedu.com · Physics Calculator Series · Unit 02: Acceleration

March 29, 2026

Velocity Calculator – Instantly Solve Speed, Distance & Time with Formulas

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Velocity Calculator

Master kinematics with our interactive velocity calculator. Solve for velocity, distance, or time instantly with unit conversions!

📐 Kinematics ⚡ Instant Results 🔄 Unit Conversion 📚 NCERT Based

📌 Core Formula

v = d ÷ t

FIND VELOCITY

v = d / t

FIND DISTANCE

d = v × t

FIND TIME

t = d / v

WITH ACCELERATION

v = u + at

🎯

Choose What to Solve

Select a mode and enter your known values

📏 Distance (d)

📏 m

⏱️ Time (t)

⏱️ s

⚡ Velocity (v)

⚡ m/s

⏱️ Time (t)

⏱️ s

📏 Distance (d)

📏 m

⚡ Velocity (v)

⚡ m/s

⚠️ Please enter valid positive numbers!

✅ Result

—

🌍

What is Velocity?

Velocity is a vector quantity describing the rate of change of position with respect to time. It has both magnitude and direction.

v = Δx / Δt

📊

Average Velocity

Average velocity is the total displacement divided by total time. It considers only the straight-line start-to-end distance.

v = (x₂−x₁)/(t₂−t₁)

⚡

Instantaneous Velocity

Velocity at a specific instant in time. It is the derivative of position with respect to time — limit of average velocity as Δt → 0.

v = dx/dt

📐

SI Unit & Dimensions

The standard unit of velocity is metre per second (m/s). Its dimensional formula is [M⁰ L¹ T⁻¹].

[M⁰ L¹ T⁻¹]

🗂️

Types of Velocity

UniformConstant speed in a straight line

Non-UniformChanging speed or direction

AverageTotal displacement ÷ total time

InstantaneousVelocity at a precise moment

RelativeVelocity w.r.t. another object

TerminalMax velocity under gravity + drag

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Variables & Symbols

All mathematical symbols used in velocity formulas

Symbol	Quantity	SI Unit	Type
v	Final Velocity	m/s	Vector
u	Initial Velocity	m/s	Vector
d / s	Distance / Displacement	m	Scalar / Vector
t	Time	seconds (s)	Scalar
a	Acceleration	m/s²	Vector
g	Gravitational Accel.	9.81 m/s²	Vector
Δx	Change in Position	m	Vector
Δt	Change in Time	s	Scalar

📌

Key Velocity Equations

Most important formulas for velocity problems

Basic Velocity

v = d / t

1st Equation of Motion

v = u + at

3rd Equation of Motion

v² = u² + 2as

Average Velocity

v = (u+v) / 2

Escape Velocity

v = √(2gR)

Relative Velocity

v_rel = v₁ − v₂

⚡ IrfanEdu.com

Free Physics Calculators for Students & Educators
irfanedu.com · Physics Calculator Series · Unit 01: Velocity

March 29, 2026

Category: Physics Calculator