Uniform Acceleration Calculator (Velocity & Displacement)
Calculate the final velocity and displacement of a uniformly accelerated linear motion from the initial velocity, acceleration, and elapsed time.
Usage Tips
- To calculate a decelerating motion, enter a negative value for acceleration (a) — for example, a = -3 when braking a vehicle to slow it down.
- Displacement (x) represents the change in position including direction, not the total distance traveled. If acceleration and initial velocity point in opposite directions, displacement can even turn negative during back-and-forth motion.
- This tool also works for free fall. Enter Earth's gravitational acceleration (about 9.8 m/s²) as the acceleration to find the velocity and distance fallen at any elapsed time after release.
- Elapsed time (t) only accepts values of 0 or greater. If you need an instant before the reference point, redefine t=0 at the moment of the initial velocity and recalculate from there.
Frequently Asked Questions
Side Note — Galileo's Discovery of the Law of Falling Bodies
The concept of uniform acceleration is generally credited to the 17th-century Italian scientist Galileo Galilei. Before him, Aristotle's belief that heavier objects fall faster had been widely accepted for centuries. Through repeated experiments rolling balls down inclined planes, Galileo showed that a falling object's speed increases at a constant rate proportional to elapsed time, regardless of its mass.
Since accurate clocks did not yet exist, Galileo is said to have measured time using his own pulse and water clocks. Because rapid falls were too fast to measure precisely, he cleverly slowed the motion down by using gently inclined planes — an approach now celebrated as a pioneering example of experimental science.
This idea of uniformly accelerated motion later evolved into Isaac Newton's equation of motion (F = ma), forming the foundation of classical mechanics. Today, the formulas for uniform acceleration are still used across many fields of engineering, from calculating a car's braking distance to designing a rocket's launch trajectory.