Speed tells you how quickly distance is covered. Velocity adds the critical missing word: the direction. They share one simple equation, but the difference between a scalar and a vector runs right through the rest of mechanics.
The Key Idea
Speed is the distance travelled per unit time, a scalar. Velocity is speed in a stated direction, a vector. Both come from v = s / t, measured in metres per second (m/s).
SECTION 01
Distance, time, and the ratio between them.
Set a constant speed and release the trolley. Watch how distance continuously grows while the object is moving. But what happens when the trolley turns around? Observe how displacement handles the return trip differently than distance.
SECTION 02
Speed, velocity, and average speed.
Speed is a scalar: 30 m/s tells you how fast, but not which way.
Velocity is a vector: 30 m/s due East is a velocity, because it states a direction.
Average speed uses the absolute totals: total distance divided by total time, regardless of any backtracking or varying speeds along the way.
Speed and velocity are not interchangeable
Two cars travelling at the exact same speed in opposite directions have different velocities, because velocity includes direction. When an exam question gives a direction, or asks about a change in direction, it is actively testing velocity. The sign (+ or -) or the compass bearing is a required part of your answer.
Worked Example
A cyclist travels 1.5 km in 5.0 minutes at a steady rate. Calculate the average speed in m/s.
Step 1 : Convert to SI units first
distance = 1.5 km = 1500 m; time = 5.0 min = 300 s.
Step 2 : Apply the equationv = s / t = 1500 m / 300 s
Step 3 : Answerv = 5.0 m/s. Converting to metres and seconds before substituting avoids the most common algebraic error here.