Falling Apples — Physics Calculator

Common Constants

g = 9.81 m/s² G = 6.674 × 10⁻¹¹ N·m²/kg² c = 3 × 10⁸ m/s 1 N = 1 kg·m/s² 1 J = 1 N·m

🏃

Final Velocity

v = u + at

Find final velocity given initial velocity, acceleration, and time.

Initial velocity u (m/s)

Acceleration a (m/s²)

Time t (s)

Final Velocity (v)

📏

Displacement

s = ut + ½at²

Find how far an object travels in a given time.

Initial velocity u (m/s)

Acceleration a (m/s²)

Time t (s)

Displacement (s)

⚡

Velocity from Displacement

v² = u² + 2as

Find final velocity without knowing time.

Initial velocity u (m/s)

Acceleration a (m/s²)

Displacement s (m)

Final Velocity (v)

💥

Newton's Second Law

F = ma

Force equals mass times acceleration.

Solve for

Mass m (kg)

Acceleration a (m/s²)

Force (F)

🌍

Weight / Gravitational Force

W = mg

Weight is the gravitational force on an object (g = 9.81 m/s² on Earth).

Mass m (kg)

Gravity g (m/s²)

Weight (W)

🧱

Friction Force

f = μN

Friction force equals coefficient of friction times normal force.

Coefficient of friction μ

Normal force N (N)

Friction Force (f)

🏎️

Kinetic Energy

KE = ½mv²

Energy an object possesses due to its motion.

Mass m (kg)

Velocity v (m/s)

Kinetic Energy (KE)

🍎

Gravitational Potential Energy

PE = mgh

Energy stored by an object due to its height — like Newton's apple on its branch.

Mass m (kg)

Height h (m)

Gravity g (m/s²)

Potential Energy (PE)

🔧

Work Done

W = Fd·cos(θ)

Work done by a force over a displacement at angle θ.

Force F (N)

Displacement d (m)

Angle θ (degrees)

Work Done (W)

🎱

Linear Momentum

p = mv

Momentum is the product of mass and velocity.

Mass m (kg)

Velocity v (m/s)

Momentum (p)

💢

Impulse

J = FΔt = Δp

Change in momentum equals force times time interval.

Force F (N)

Time interval Δt (s)

Impulse (J)

🔄

Perfectly Inelastic Collision

v' = (m��u₁ + m₂u₂) / (m�� + m₂)

Two objects collide and move together after impact.

Mass 1 m₁ (kg)

Velocity 1 u₁ (m/s)

Mass 2 m₂ (kg)

Velocity 2 u₂ (m/s)

Combined Velocity after collision (v')

🚀

Projectile Motion

x = v₀cos(θ)·t | y = v₀sin(θ)·t − ½gt��

Calculates range, max height, and time of flight for a projectile launched from ground level.

Launch speed v₀ (m/s)

Launch angle θ (degrees)

Gravity g (m/s²)

Results

🌰

Free Fall

h = ½gt²

Like Newton's apple — dropped from rest, how far does it fall?

Time falling t (s)

Gravity g (m/s²)

Distance Fallen

📊

Average Velocity

v_avg = (u + v) / 2

Mean of initial and final velocity (constant acceleration only).

Initial velocity u (m/s)

Final velocity v (m/s)

Average Velocity

📈

Average Acceleration

a = (v − u) / t

Rate of change of velocity over time.

Initial velocity u (m/s)

Final velocity v (m/s)

Time t (s)

Acceleration (a)

🛑

Stopping Distance

d = v² / (2a)

Distance needed to decelerate from velocity v to rest.

Initial speed v (m/s)

Deceleration a (m/s²)

Stopping Distance (d)

🔵

Centripetal Acceleration

a_c = v² / r

Inward acceleration of an object in circular motion.

Speed v (m/s)

Radius r (m)

Centripetal Acceleration (a_c)

🌀

Centripetal Force

F_c = mv² / r

Net inward force required to maintain circular motion.

Mass m (kg)

Speed v (m/s)

Radius r (m)

Centripetal Force (F_c)

🔄

Angular Velocity

ω = 2π / T

Rate of rotation in radians per second from period T.

Period T (s)

Angular Velocity (ω)

↗️

Linear Speed from Angular Velocity

v = ωr

Convert rotational speed to linear (tangential) speed.

Angular velocity ω (rad/s)

Radius r (m)

Linear Speed (v)

⏱️

Period of Revolution

T = 2πr / v

Time for one complete circular orbit.

Radius r (m)

Speed v (m/s)

Period (T)

🏔️

Time to Maximum Height

t = v₀ · sin(θ) / g

Time for a projectile to reach its peak height.

Launch speed v₀ (m/s)

Launch angle θ (degrees)

Gravity g (m/s²)

Time to Max Height (t)

🚗

Relative Velocity (1D)

v_rel = v₁ − v₂

Speed of object 1 as seen by object 2 along the same axis.

Velocity of object 1 v₁ (m/s)

Velocity of object 2 v₂ (m/s)

Relative Velocity (v_rel)