What is Velocity? Definition, Formula, SI Unit, Types & Solved Examples

If a car travels 100 km and comes back to the same point, its speedometer records 200 km, yet its displacement is zero. Speed says the car moved a lot. Velocity says it got nowhere. This difference is the starting point for understanding what velocity really means in physics.

Velocity is the rate of change of displacement with time. Because displacement has both magnitude and direction, velocity is a vector quantity. The velocity meaning in everyday language is simply "how fast something moves in a particular direction".
Saying a train moves at 80 km/h gives its speed. Saying it moves at 80 km/h towards the north gives its velocity.

The basic velocity formula is:
v = Displacement / Time = Δx / Δt
For motion that changes with time, the instantaneous velocity is the derivative of displacement:
v = dx/dt
The average velocity formula uses total displacement over total time:
v(avg) = (x₂ - x₁) / (t₂ - t₁)
When acceleration is uniform, average velocity can also be written as v(avg) = (u + v)/2, where u is the initial velocity and v is the final velocity.

The SI unit of velocity is metre per second (m/s or m s⁻¹). The common practical unit is kilometre per hour (km/h), and 1 km/h equals 5/18 m/s, or about 0.278 m/s.
The dimension of velocity is [M⁰L¹T⁻¹], since it is length divided by time.

Students are often asked to distinguish between speed and velocity in exams. Here is the comparison:

In the speed vs velocity comparison, the key point is direction. A car moving in a circle at a steady 40 km/h has constant speed, yet its velocity keeps changing because its direction keeps changing.

Below mentioned are the different types of velocity.
1. Uniform velocityAn object has uniform velocity when it covers equal displacements in equal intervals of time along a straight line. Both magnitude and direction stay constant, so acceleration is zero.
2. Non-uniform (variable) velocityHere either the magnitude or the direction changes with time. A car in city traffic and a stone in projectile motion both show non-uniform velocity.
3. Average velocityThis is total displacement divided by total time. It ignores everything that happened in between.
4. Instantaneous velocityThis is the velocity at one particular instant, given by dx/dt. The reading on a speedometer is the magnitude of instantaneous velocity.
5. Relative velocityThis is the velocity of one object as seen from another. For two objects moving along a line, v(AB) = v(A) - v(B).
6. Angular velocityFor circular motion, angular velocity (ω) is the rate of change of angular displacement: ω = θ/t = 2π/T. Its SI unit is radian per second, and it links to linear velocity through v = rω.
7. Drift velocityIn a current-carrying conductor, electrons move slowly in one direction under an electric field. The drift velocity formula is:
v(d) = I / (nAe)
Here I is the current, n is the number of free electrons per unit volume, A is the area of cross-section, and e is the electronic charge. Drift velocity is typically less than 1 mm/s, which is why it appears in almost every Current Electricity chapter.

Yes to both. Velocity is negative when the object moves opposite to the chosen positive direction. If you take the rightward direction as positive, a body moving leftwards has negative velocity.
Velocity becomes zero when displacement is zero, even if the object has been moving. A person who walks around a park and returns to the starting point has zero average velocity for the whole trip, although the average speed is clearly not zero. A ball thrown upward also has zero velocity for an instant at its highest point.

Example 1: Average velocity A car travels 60 km east in 1 hour, then 40 km west in 1 hour. Total displacement = 60 - 40 = 20 km east. Total time = 2 h. Average velocity = 20/2 = 10 km/h east. Average speed = 100/2 = 50 km/h. The two answers differ because displacement is smaller than distance.
Example 2: Instantaneous velocity If x = 5t² + 3t metres, then v = dx/dt = 10t + 3. At t = 2 s, v = 10(2) + 3 = 23 m/s.
Example 3: Angular velocity of a minute hand A minute hand completes one rotation in 60 minutes, so T = 3600 s. ω = 2π/T = 2 × 3.14 / 3600 = 1.745 × 10⁻³ rad/s. For comparison, the hour hand takes 12 hours, giving ω = 1.454 × 10⁻⁴ rad/s.
Example 4: Unit conversion Convert 72 km/h into m/s. 72 × 5/18 = 20 m/s.

Velocity is displacement per unit time, and its vector nature is what separates it from speed. Once you are comfortable with the average and instantaneous forms, the other types of velocity become easier to place. Practise converting units and solving displacement-based numericals, since most exam questions test exactly these two skills.