Calculator Suite

Velocity-Squared Calculator

Calculate velocity, initial velocity, acceleration, or displacement using v² = u² + 2as

Velocity-Squared Problem Setup
Use v² = u² + 2as to solve for final velocity, initial velocity, acceleration, or displacement

Select which variable you want to calculate

Known Variables

Enter initial velocity in m/s

Enter acceleration in m/s²

Enter displacement in m

Common Scenarios

Vehicle Stopping Distance

How far to stop from highway speed?

Launch Acceleration

What acceleration needed to reach target velocity?

Impact Velocity

Velocity after falling a certain distance

Quick Presets

Earth Gravity (-9.81 m/s²)
Velocity Squared Formula
The "Timeless" Equation of Motion

The Equation

v2=u2+2asv^2 = u^2 + 2as

Calculates final velocity squared without needing time (tt).

Variables

  • vv = Final Velocity
  • uu = Initial Velocity
  • aa = Acceleration
  • ss = Displacement
Understanding Velocity Squared

TL;DR

This formula (v2=u2+2asv^2 = u^2 + 2as) calculates velocity without knowing time. It's essential for finding stopping distances or impact speeds given a specific distance.

The "Timeless" Equation

This equation relates velocity to displacement directly, skipping the time variable. It connects Kinematics with the Work-Energy Principle.

How to Use This Calculator

  1. Choose Variable: Select what you need to find (e.g., "Final Velocity").
  2. Enter Knowns: Input the values you have (Initial Velocity, Acceleration, Displacement).
  3. Watch Signs: If slowing down, acceleration and velocity must have opposite signs.
  4. Calculate: Get the result and see step-by-step math.

Real-World Example: The "Squared" Danger

Scenario:

A car doubles its speed from 30 km/h to 60 km/h. How does braking distance change?

Analysis:

  • Formula: Stopping distance s∝v2s \propto v^2.
  • Result: 22=42^2 = 4. Braking distance quadruples (4x)!

3 Key Checks (The "SOP")

Sign Check

Braking? aa and uu must have opposite signs.

Math Check

Negative inside \sqrt{}? Impossible. Check your inputs.

Unit Check

Don't mix km/h and meters. Convert all to SI (m/s) first.

Assumptions & Limitations

  • Constant Acceleration: The formula is invalid if aa changes.
  • Linear Path: Assumes motion along a straight line.
  • No imaginary numbers: Real-world physics doesn't allow square roots of negatives here.

Video Tutorials

Kinematic Equations: No Time (Khan Academy)

Stopping Distance Physics

Frequently Asked Questions

When should I use this formula?

Use v2=u2+2asv^2 = u^2 + 2as when you don't know the time and aren't asked to find it. It relates velocities directly to distance.

Why can't I calculate the square root of a negative?

In the real world, you can't have "imaginary" velocity. If the math gives a negative inside the square root, it usually means the object would have stopped earlier than the distance you entered.

Does this apply to falling objects?

Yes! For a dropped object, u=0u=0 and a=ga=g. The formula becomes v=2gsv = \sqrt{2gs}, which is the speed of impact after falling distance ss.

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Linear Motion CalculatorDisplacement CalculatorForce CalculatorKinetic Energy Calculator