Velocity Calculator

Understanding the velocity equation

This calculator uses one of the core equations of motion: final velocity equals starting velocity plus acceleration times time. It applies whenever acceleration is steady, which covers a huge range of everyday physics, from a car speeding up to an object falling under gravity.

Here v is the final velocity, v₀ is the initial velocity, a is the acceleration, and t is the time elapsed.

How to use this calculator

1. Enter the initial velocity, \(v_0\), in the chosen units.
2. Enter the acceleration, \(a\), in units per time squared, such as \(\mathrm{m/s^2}\).
3. Enter the time, \(t\), in seconds or the time unit used in your problem.
4. Click calculate to get the final velocity, \(v\).

The formula explained

The formula \(v = v_0 + at\) computes the final velocity after an object has accelerated for a given time. It adds the change in velocity, \(at\), to the starting velocity, \(v_0\).

• v = final velocity
• \(v_0\) = initial velocity
• a = acceleration
• t = time

Step by step method

1. Start with the initial velocity, \(v_0\).
2. Multiply acceleration, \(a\), by time, \(t\), to find the change in velocity.
3. Add that change to \(v_0\) using \(v = v_0 + at\).

Worked example

Problem. A car starts with an initial velocity of \(12\,\mathrm{m/s}\), accelerates at \(3\,\mathrm{m/s^2}\), for \(4\,\mathrm{s}\). Find the final velocity.

1. Use \(v = v_0 + at\).
2. Substitute the values, \(v = 12 + 3 \times 4\).
3. Compute \(3 \times 4 = 12\), so \(v = 24\,\mathrm{m/s}\).

Tips and common mistakes

• Make sure the time unit matches the acceleration unit, because \(a\) and \(t\) must work together correctly.
• A negative acceleration means the velocity decreases, so the final velocity can be smaller than the initial velocity.

Frequently asked questions