Third Equation of Motion Calculator

Calculate final velocity using v² = u² + 2as

Kinematics Calculator

The third equation of motion (v² = u² + 2as) relates final velocity (v), initial velocity (u), acceleration (a), and displacement (s). Enter any three values to calculate the missing one.

v² = u² + 2as
Velocity at the start of motion
Velocity at the end of motion
Rate of change of velocity
Distance traveled in a given direction
Motion Visualization

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Tool Features
Real-time Calculation

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Unit Conversion

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Calculation History

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Visualization

Graphical representation of motion

Step-by-step Solution

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Understanding the Third Equation of Motion

The third equation of motion is a fundamental formula in kinematics that relates the final velocity of an object to its initial velocity, acceleration, and displacement. This equation is essential for solving problems in physics where time is not given or not needed.

The Equation: v² = u² + 2as

Where:

How to Use This Calculator

  1. Enter three known values: Fill in any three of the four variables (initial velocity, acceleration, displacement, or final velocity).
  2. Select appropriate units: Use the dropdown menus to select the correct units for each measurement.
  3. Click "Calculate": The calculator will automatically compute the missing value using the third equation of motion.
  4. Review the results: Examine the detailed solution to understand how the calculation was performed.
  5. Save if needed: You can save the calculation to your history for future reference.

Practical Applications

The third equation of motion is widely used in various fields:

Automotive Engineering

Calculating braking distances or acceleration capabilities of vehicles.

Aerospace

Determining runway lengths needed for aircraft takeoff and landing.

Sports Science

Analyzing athlete performance in track events or cycling.

Education

Teaching fundamental physics concepts in classrooms and laboratories.

Important Notes
  • This equation assumes constant acceleration.
  • All units must be consistent for accurate results.
  • Displacement refers to the change in position, not necessarily the total distance traveled.
  • Negative acceleration indicates deceleration or slowing down.