Velocity Calculator



\[ v = \dfrac{s}{t} \]

Easily calculate velocity using multiple powerful physics formulas in one place.

Whether you’re solving for basic speed (v = s/t), final velocity (v = u + at), or using advanced equations like v = √(u² + 2as) and average velocity, this calculator delivers fast, accurate, and step-by-step results.

Perfect for students, teachers, and anyone exploring motion in physics.

Basic Velocity (v = s/t)

This is the most basic and commonly used formula for velocity, especially when the motion is uniform. Uniform motion means the object is moving with constant velocity, without any change in speed or direction.

The formula is,

\[ \boxed{v = \frac{s}{t}} \]

Here, \(s\) represents displacement and \(t\) represents time. This formula tells us how much displacement occurs in each unit of time.

From Acceleration & Time (v = u + at)

When an object is not moving with constant velocity, but instead its velocity is changing over time, we introduce acceleration. In such cases, this formula becomes extremely useful.

\[a=\dfrac{v-u}{t}\]

\[at=v-u\]

\[\boxed{v=u + at}\]

Here, \(u\) is the initial velocity, \(a\) is acceleration, and \(t\) is time. This equation tells us how velocity evolves over time under constant acceleration.

From Acceleration & Distance (v² = u² + 2as)

This formula is especially useful when time is not given in the problem, but displacement is known. It connects velocity directly with displacement and acceleration.

\[
v = u + at
\]

\[
s = \frac{(u+v)}{2} \, t
\]

From the first equation:

\[
t = \frac{v – u}{a}
\]

Substitute into second equation:

\[
s = \frac{(u+v)}{2} \cdot \frac{v-u}{a}
\]

\[
s = \frac{v^2 – u^2}{2a}
\]

Finally,

\[
\boxed{v^2 = u^2 + 2as}
\]

Calculate Average Velocity

Average velocity becomes important when motion is not uniform, meaning velocity keeps changing during the journey. One common exam case is when an object travels equal distances at different velocities.

\[
v_{avg} = \dfrac{\text{total distance}}{\text{total time}} = \dfrac{2d}{\dfrac{d}{v_1} + \dfrac{d}{v_2}}
\]

\[
= \dfrac{2d}{d\left(\dfrac{1}{v_1} + \dfrac{1}{v_2}\right)} = \dfrac{2}{\dfrac{1}{v_1} + \dfrac{1}{v_2}}
\]

\[
\boxed{v_{avg}= \dfrac{2 v_1 v_2}{v_1 + v_2}}
\]