Final velocity calculator
Starting at 10 m/s and accelerating at 2 m/s² for 5 s, an object ends up at 20 m/s. Enter the initial velocity, the acceleration and the elapsed time, with signs for slowing down or reversing, to get the final velocity. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Initial velocity
- 10
- Constant acceleration
- 2
- Elapsed time
- 5
- Voltage (V)
- 20
- Final velocity
- 20
- Equation
- v = 10 + (2) · (5) = 20
A final velocity calculator applies the first constant-acceleration kinematics equation: final velocity v equals initial velocity u plus acceleration a times elapsed time t. Enter three finite numbers—u (initial velocity), a (constant acceleration), and t (non-negative time)—and the tool returns the rounded final velocity, a readable substitution equation, a short physics message, and ordered step strings you can paste into homework checks or automated tests. Deceleration, reverse direction, and uniform motion (a equals zero) are all supported through signed u and a.
What v = u + a t means in constant-acceleration kinematics
Under constant acceleration the velocity of a particle changes at a fixed rate. If the velocity at the start of an interval is u and the acceleration remains a for a duration t, the velocity at the end of that interval is exactly v equals u plus a times t. This is the first of the standard SUVAT equations taught in introductory mechanics: it relates only velocity, acceleration, and time, and does not require knowing displacement.
Initial velocity u may be positive or negative depending on the chosen positive direction; acceleration a may likewise be positive (speeding up in the positive direction) or negative (deceleration or acceleration opposite the positive axis). Time t is the elapsed duration of the interval and must be non-negative for this calculator—negative t would reverse the causal reading of “after time t” that learners search for when they look up a final velocity calculator. When t is zero there is no interval, so v equals u by definition.
When a is zero the motion is uniform and velocity never changes. The tool does not convert units: if u is in metres per second and a is in metres per second squared, t must be in seconds so that a times t has the same unit as u and their sum is a consistent velocity.
The same rule applies in any coherent system—feet per second and feet per second squared, kilometres per hour with time in hours after converting acceleration accordingly—so callers keep one system end to end rather than mixing SI and imperial mid-equation.
Practical tips, limits, and related searches
Use a consistent unit system for all three inputs before calling; this landing does not perform unit conversion. When teaching direction conventions, keep the sign of a aligned with the positive axis you chose for u rather than treating “slowing down” as always negative without defining axes.
This page targets people searching for a final velocity calculator, v equals u plus a t, or constant-acceleration kinematics online; it is not a full SUVAT suite that also solves for displacement or time given mixed unknowns, not a variable-acceleration integrator, and not a unit converter. Prefer this capability when you already know initial velocity, constant acceleration, and elapsed time and only need the final velocity; if your source problem gives displacement instead of time, rearrange another kinematic equation first.
Round-trip checks are easy: recompute u plus a times t by hand and confirm it equals the published v within the same twelve-decimal rounding used in the response.
What you can do with it
Homework checks for SUVAT velocity
Students enter u, a, and t from textbook constant-acceleration problems and compare hand-written v and substitution steps against a deterministic result before submitting.
Quick lab pre-check before full motion solvers
Pipelines validate final velocity from u, a, and t first, then branch to displacement or multi-segment trajectories only when the single-interval check matches lab notes.
FAQ
What formula does the final velocity calculator use?
It uses the constant-acceleration equation v = u + a t, where u is initial velocity, a is acceleration, and t is elapsed time.
Why is negative time rejected?
Elapsed time cannot be negative in this model.
Can acceleration be negative?
Yes. Negative a means deceleration or acceleration opposite your positive direction. Only t is required to be non-negative.
Does this convert units for me?
No. Keep u, a, and t in one consistent unit system (for example m/s, m/s², and s). The calculator only evaluates v = u + a t.
Is the final velocity calculator free?
The browser tool is free and runs locally.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/mech/kinematics-velocity \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"u":10,"a":2,"t":5}'const res = await fetch("https://api.kit.forhosting.com/mech/kinematics-velocity", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"u": 10,
"a": 2,
"t": 5
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/mech/kinematics-velocity",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"u": 10,
"a": 2,
"t": 5
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/mech/kinematics-velocity", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"u":10,"a":2,"t":5}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"u":10,"a":2,"t":5}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/mech/kinematics-velocity", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"u": 10,
"a": 2,
"t": 5
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "mech.kinematics_velocity",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Limits
max_abs | 1000000000000 |
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
Negative time is rejected with a clear invalid_input error because elapsed duration cannot run backward in this model; zero time correctly returns v equals u. Pricing is a flat $0.002 per successful API request; failed validation is never charged.
How to call the API and what comes back
Absolute values of u and a must stay within the published limit of one trillion; t must be between zero and one trillion inclusive. Send a JSON body with three required finite numbers: u (aliases initial_velocity, u0, and v0), a (aliases acceleration and accel), and t (aliases time and duration). Failed validation—missing fields, non-finite numbers, values outside absolute limits, a non-finite product, a final velocity outside the absolute cap, or negative t—returns invalid_input and is never charged. Pricing is a flat $0.002 per successful request with unit item and zero marginal unit price. Prefer sending JSON numbers when you control the client; string numbers are accepted only when they match a strict finite numeric pattern, which keeps homework-form paste paths working without accepting arbitrary text.
Practical tips, limits, and related searches
Keep u, a, and t inside the published absolute range so the product a times t and the sum u plus a t remain finite in IEEE double precision on the Worker and in the browser. Pair classroom examples deliberately: u equals ten, a equals two, t equals five yields v equals twenty; u equals twenty, a equals negative four, t equals three yields deceleration to eight; u equals five, a equals zero, t equals twelve demonstrates uniform motion; and t equals negative one demonstrates the hard invalid_input path for negative time. Failed tasks that return invalid_input do not consume prepaid balance, which keeps exploratory scripts cheap when learners deliberately pass negative t.
Integration use cases
Unit tests for physics engine helpers
Generate known-good accelerate, decelerate, and zero-time cases plus deliberate negative-time rejections for coding kata expected values in games or simulators.