What is initial velocity?

Initial velocity (u) is the speed of an object at the start of a time interval, before any acceleration acts on it. In kinematic equations it is always denoted u, as opposed to v for final velocity.

What formulas does this calculator use?

Method 1 rearranges the first kinematic equation: u = v − a × t. Method 2 rearranges the third kinematic equation: u = √(v² − 2 × a × s). Both assume constant (uniform) acceleration.

Can initial velocity be negative?

Yes. A negative initial velocity means the object starts moving in the direction opposite to the chosen positive axis. This calculator accepts and returns negative values correctly.

What if the value under the square root is negative in Method 2?

A negative value under the radical means the inputs are physically inconsistent — for example, the object cannot have traveled that distance while decelerating from that final speed. The calculator will display an error and ask you to recheck the values.

Does this assume constant acceleration?

Yes. Both kinematic equations used here require acceleration to be constant throughout the motion. For variable acceleration, integration-based methods are needed.

What units are supported?

Velocity: m/s, km/h, mph, ft/s. Acceleration: m/s², g (9.80665 m/s²), ft/s². Time: seconds, minutes, hours. Distance: meters, kilometers, miles, feet. The calculator converts all inputs to SI before computing.

Initial Velocity Calculator

Name: Initial Velocity Calculator
Availability: InStock
Author: Nham Vu

Solve for initial velocity using kinematic equations — enter final velocity, acceleration, and either time or distance.

Initial Velocity Calculator

Method

Final Velocity (v)

Acceleration (a)

Time (t)

Enter values on the left to compute initial velocity.

u = v − a × t — Uniform Acceleration

Copied!

Summary

Solve for initial velocity using kinematic equations — enter final velocity, acceleration, and either time or distance.

How it works

Select a calculation method: time-based (u = v − at) or distance-based (u = √(v² − 2as)).
Enter the final velocity (v), acceleration (a), and either time (t) or distance (s).
Choose your preferred units for each quantity using the dropdowns.
Click Calculate (or type and press Enter) to see the initial velocity with worked steps.
Click any conversion tile to copy that value to your clipboard.
Use Clear to reset inputs or Reset to switch methods.

Use cases

Determine how fast a ball was thrown given its final speed after acceleration.
Find a vehicle's initial speed before braking, given deceleration and stopping distance.
Solve high-school and university kinematics problems.
Verify physics homework answers with step-by-step workings.
Analyze sports motion — a sprint start, a javelin release, or a bicycle brake.
Engineering: back-calculate launch speed from impact data.
Understand projectile motion by isolating the initial velocity component.
Convert results between m/s, km/h, mph, and ft/s automatically.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu