What is the difference between velocity and speed

Speed measures how much ground an object covers per unit time, ignoring any notion of direction. It is calculated as the total distance traveled divided by the elapsed time and is expressed as a single positive number, such as 60 km/h. Velocity, on the other hand, requires both a magnitude and a direction; it is the displacement (the straight‑line change in position) divided by the same time interval and is written as a vector, for example 60 km/h north.

Key Differences

Main contrasts between speed and velocity:

• Speed is a scalar quantity; velocity is a vector
• Speed uses total distance; velocity uses net displacement
• Speed is always non‑negative; velocity can be positive, negative, or zero depending on direction
• Speed tells how fast; velocity tells how fast and where

Direction matters because displacement can be zero even when distance is large. If you run a 400‑m lap and end up where you started, your speed might be 4 m/s but your average velocity is 0 m/s because the net change in position is zero. This distinction explains why cyclists can have the same speed on a circular track yet have different velocities if one rides clockwise and the other counter‑clockwise.

To compute speed and velocity:

1. 1Measure the total distance traveled during the interval
2. 2Measure the straight‑line displacement between start and end points
3. 3Divide each measurement by the same elapsed time

Worked example: A car drives 100 km east in 2 h. Speed = $\frac{100\text{ km}}{2\text{ h}} = 50\text{ km/h}$. Displacement is also 100 km east, so velocity = $\frac{100\text{ km east}}{2\text{ h}} = 50\text{ km/h east}$. If the car then returns 40 km west in the next hour, total distance becomes 140 km and total time 3 h, giving a new speed of $\frac{140}{3}\approx46.7\text{ km/h}$. Net displacement is 60 km east, so new velocity = $\frac{60\text{ km east}}{3\text{ h}} = 20\text{ km/h east}$. This illustrates how speed and velocity diverge when the path is not straight.

Speed versus velocity for two trips:

In physics problems, always decide whether the question asks for a scalar (speed) or a vector (velocity). Use distance for speed calculations and displacement for velocity calculations. Remember that vectors can be added, subtracted, or broken into components, while scalars cannot, which often simplifies motion analysis.